Copy and complete each of the equalities below using the options given. √2 0 11/2 √/3 2/2 ¹(√³)=C₂0⁰ CL a) tan 45º = b) sin-1 √3 2 1 √3 30° 45° 60° 90°​

well, we know its center and a point on the circle, well, the distance from the center to a point on it is well, you guessed it!! is its radius.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-7}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~1 - (-7)~~)^2 + (~~-8 - (-2)~~)^2} \implies r=\sqrt{(1 +7)^2 + (-8 +2)^2} \\\\\\ r=\sqrt{( 8 )^2 + ( -6 )^2} \implies r=\sqrt{ 64 + 36 } \implies r=\sqrt{ 100 }\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-7}{h}~~,~~\underset{-2}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-7) ~~ )^2 ~~ + ~~ ( ~~ y-(-2) ~~ )^2~~ = ~~10^2\implies (x+7)^2 + (y+2)^2 = 100[/tex]

36 is the range of the score.

The data set's smallest score is 64, as indicated in the key, and its highest score is 100. (which is the last value in the stem-and-leaf plot).

The range of scores is as follows:

Range: Maximum score - Minimum score

Range = 100 - 64

Range = 36

The range of scores is therefore 36.

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Complete question:

The volume of water displaced by the unknown mass (x) rock is 331 ml

What is meant by displaced?

Displaced means to be moved or forced out of its original position or location. It can refer to a physical object or a person who has been forced to leave their home or community due to conflict, natural disaster, or other circumstances. Displacement can cause significant challenges and disruptions to individuals and communities.

According to the given information

The formula for water displacement is: Volume (object) = Volume (water + object). This formula is based on Archimedes’ Principle, which states that the weight of the displaced fluid is equal to the weight of the submerged object1.

So, we can calculate the volume of water displaced by the unknown mass (x) rock as follows:

Volume (water + object) = 471 ml Volume (water) = 140 ml Volume (object) = Volume (water + object) - Volume (water) Volume (object) = 471 ml - 140 ml Volume (object) = 331 ml

Therefore, the volume of water displaced by the unknown mass (x) rock is 331 ml

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The volume of a right circular cylinder with a diameter of 6 meters and a height of 14 meters as required is; 54π.

It follows from the task content that the volume of a cylinder whose diameter is 6 meters and height is 14 meters.

Since the volume of a right circular cylinder is given by; V = πr²h.

since Diameter is; 6 ft. Radius, r = 6/2 = 3 meters.

Volume, V = π (3)² 6; V = π × 9 × 6

Volume, V = 54π.

Ultimately, the volume of the right circular cylinder is; 54π m³.

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The audience of each of the four organizations at the end of that year is found by solving the equations given as :

x = 49 million, y = 22 million, z = 21 million and u = 20 million.

Given that,

Combined audience = 112 million

x + y + z + u = 112 [Equation 1]

Other equations are,

y - z = z - u [Equation 2] ⇒ y + u = 2z

Substituting this in [Equation 1],

x + 3z = 112 [Equation 5]

x - y = 3(y - u) + 21 [Equation 3]

x - y + z - u = 28 [Equation 4]

x - y + y - z = 28

x - z = 28 [Equation 6]

Solving [Equation 5] and [Equation 6],

z = 21 and x = 49

Substituting, Equation 1 becomes,

y + u = 42

From Equation 3,

4y - 3u = 28

Solving these two equations,

u = 20 and y = 22

Hence x = 49 million, y = 22 million, z = 21 million and u = 20 million.

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sinθ=y/r

cosθ=x/r

tanθ=y/x

x^2 + y^2 = r^2

r^2(sin^2 θ + cos^2 θ) =r^2

sin^2 θ + cos^2 θ=1

Answer:

22 + 5x - 10 = 90

5x + 12 = 90

5x = 78

x = 15.6

Answer:

((.67 - (2/3))/(2/3))(100%) = .5%

Answer:

Sure. Here are the steps on how to calculate the interest and balance reduction for Poppy's first mortgage payment:

Calculate the monthly interest rate.

The monthly interest rate is calculated by dividing the annual interest rate by 12. In this case, the annual interest rate is 4.9%, so the monthly interest rate is:

monthly interest rate = 4.9% / 12 = 0.41%

Calculate the interest paid for the first month.

The interest paid for the first month is calculated by multiplying the monthly interest rate by the outstanding loan balance. In this case, the outstanding loan balance is $180,000, so the interest paid for the first month is:

interest paid = 0.41% * $180,000 = $738

Calculate the principal amount of the first payment.

The principal amount of the first payment is calculated by subtracting the interest paid from the monthly payment. In this case, the monthly payment is $955.31 and the interest paid is $738, so the principal amount of the first payment is:

principal amount = $955.31 - $738 = $217.31

Calculate the balance after the first payment.

The balance after the first payment is calculated by subtracting the principal amount from the outstanding loan balance. In this case, the outstanding loan balance is $180,000 and the principal amount of the first payment is $217.31, so the balance after the first payment is:

balance after first payment = $180,000 - $217.31 = $177,782.69

Therefore, the interest paid in month one is $738 and the balance reduced after the first payment is $217.31.

Step-by-step explanation:

The median score on the quiz is 10. The answer is (d)10.

We must arrange the scores from lowest to highest in order to determine the median score. The cumulative frequency for each score can also be calculated.

Score Frequency Cumulative Frequency

5                     1                                     1

6                     2                                    3

7                     5                                    8

8                     5                                    13

9                     7                                    20

10                   10                                   30

The score that distinguishes the upper half of the scores from the lower half is the median, or middle score. Since there are 30 scores, the center score is the fifteenth score.

We can begin by adding the frequencies until we reach or exceed the 15th position in order to accomplish this:

Scores 5 and 6 have a cumulative frequency of 3 (1 + 2)

Scores 7 and 8 have a cumulative frequency of 13 (8 + 5)

Therefore, the median score must be in the 9-10 range. We can further break down this range to find the exact median value:

The cumulative frequency of score 9 is 20, indicating that it is not the median value.

Score 10 has a combined recurrence of 30, which is more noteworthy than the fifteenth position.

As a result, this dataset's median score is 10.

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The median of the statistics quiz will be 9.

What is median ?

The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.

To find the median score on the quiz, we need to arrange the scores in order from lowest to highest. Using the frequency table, we can write out all the scores:

5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

There are 30 scores in total, so the median will be the average of the 15th and 16th scores (in order).

So, the median score on the quiz is:

(9 + 9) / 2 = 9

Hence the median of the statistics quiz will be 9.

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The graph shows a linear relationship where the value of the car decreases as time passes. We can see that after 0 years (when the car is brand new), its value is $30,000, and after 10 years, its value is $5,000.

We can use the slope-intercept form of a linear function (y = mx + b), where m is the slope and b is the y-intercept, to find the function that represents this relationship.

The slope is found by taking the difference in y-values (change in value) divided by the difference in x-values (change in time):

slope = (5000 - 30000) / (10 - 0) = -2500

The y-intercept is the value of the car when it is brand new, which is $30,000.

So, the equation of the line is:

y = -2500x + 30000

This matches the form of the equation y = -3000x + 27000, which is option (D), after we simplify it by combining the constants:

y = -3000x + 27000 = -2500x + 30000

Therefore, the function that best represents the relationship shown in the graph is y = -3000x + 27000.

Answer:

So, we can write the equation:

2.2x = 132

To solve for x, we can divide both sides by 2.2:

x = 132 ÷ 2.2

x = 60

Therefore, 220% of 60 is 132

The measure of center and measure of spread are 163.5 and 39 Respectively.

Measure of centre is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution.

Therefore we can say that measure of centre is the average or mean of the data.

(190+187+186+183+182+182+181+181+180+180+161+164+160+160+160+158+156+155+152.5+151)/20

= 3269.5/20

= 163.5

therefore measure of center is 163.5

The measure of spread is the range of the data.

range = 190-151 = 39

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The quadratic equation on the given graph can be written as:

y = (x + 2)*(x - 1)

Here we have the graph of a quadratic equation, we can see that the roots of the quadratic are:

x = -2 and x = 1.

Then if the leading coefficient is a, we can write the factorized form as:

y = a*(x + 2)*(x - 1)

We also know that the y-intercept is (0, -2), replacing these values we will get:

-2= a*(0 + 2)*(0 - 1)

-2 = a*-2

-2/-2 = a

1 = a

The quadratic equation is:

y = (x + 2)*(x - 1)

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The closest ten thousand to 1,210,000 is 1,210,000 itself.

To find the lowest and largest number of people that could have visited London, we need to determine the range of possible values within which 1,210,000 falls.

If we round 1,210,000 to the nearest hundred thousand, we get 1,200,000. This means that the actual number of visitors could be up to 50,000 more than 1,200,000 or up to 10,000 less than 1,200,000.

Therefore, the lowest number of people that could have visited London is:

1,200,000 - 50,000 = 1,150,000

And the largest number of people that could have visited London is:

1,200,000 + 10,000 = 1,210,000

So the lowest number of people that could have visited London is 1,150,000, and the largest number is 1,210,000.

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of line

Answer:

y= -0.5x + 2 (I think)

Step-by-step explanation:

y =mx + c

gradient is -0.5 because society

m = -0.5

y intercept is 2 because 2

so that means answer swag

The average age of the animals at an animal rescue is 5.2 months

The average or mean of the data is defined as the ratio of the sum of observations to the total number of observations recorded

Given in the question,

Dogs = 30%

Cats = 70%

Age of dogs = 8 months

Age of cats = 4 months

Suppose the number of animals at the animal rescue is 100, then

Number of cat = 70

Number of dogs = 30

Average = 70 * 4 + 30 * 8 / 100

= 280 + 240 / 100

= 520 / 100

= 5.2 months

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Given: $f(x) = \log(3x + 3 - 2x - 2)$

We need to prove that: $\frac{(a+b)^2}{f(a)+f(b)} = -4$

First, we need to simplify $f(x)$:

$f(x) = \log(x+1)$ (by simplifying the expression inside the log)

Now, we can rewrite the expression we need to prove as:

$\frac{(a+b)^2}{\log(a+1) + \log(b+1)} = -4$

Using the property of logarithms, we can rewrite this as:

$\log((a+1)(b+1)) = \log(e^{-4})$

Simplifying further:

$(a+1)(b+1) = e^{-4}$

Expanding the left side and simplifying:

$ab + a + b + 1 = e^{-4}$

Now, we can use the identity $(a+b)^2 = a^2 + 2ab + b^2$:

$(a+b)^2 = a^2 + 2ab + b^2$

Dividing both sides by $f(a)+f(b)$, which is $\log(a+1) + \log(b+1)$:

$\frac{(a+b)^2}{\log(a+1) + \log(b+1)} = \frac{a^2 + 2ab + b^2}{\log(a+1) + \log(b+1)}$

Using the property of logarithms again, we can simplify the denominator:

$\frac{(a+b)^2}{\log((a+1)(b+1))} = \frac{a^2 + 2ab + b^2}{\log((a+1)(b+1))}$

Substituting the value we derived earlier for $(a+1)(b+1)$:

$\frac{(a+b)^2}{\log(e^{-4})} = \frac{a^2 + 2ab + b^2}{\log(e^{-4})}$

Simplifying:

$(a+b)^2 = a^2 + 2ab + b^2$

$4ab = -4$

Dividing both sides by 4:

$ab = -1$

Therefore, we have shown that $\frac{(a+b)^2}{f(a)+f(b)} = -4$ if $f(x) = \log(3x+3-2x-2)$.

By increasing the number of wire turns, using a thicker wire, increasing the battery voltage, and using a soft iron core, the student can enhance the electromagnet's strength, allowing it to pick up more paper clips.

To increase the number of paper clips the electromagnet will pick up, the student should take the following actions:

1. Increase the number of wire turns: By wrapping the wire around the iron nail more times, the student will create a stronger magnetic field. This is because each wire turn generates a magnetic field, and when the turns are in close proximity, their fields add up, creating a stronger overall field.

2. Use a thicker wire: A thicker wire will allow more current to flow through it, which will result in a stronger magnetic field. The higher the current, the more powerful the electromagnet becomes.

3. Increase the voltage of the battery: By increasing the voltage of the battery, the student can cause more current to flow through the wire. This will enhance the magnetic field, making the electromagnet more effective at picking up paper clips.

4. Use a soft iron core: Soft iron materials have higher magnetic permeability than other materials, meaning they can easily be magnetized and demagnetized. When the wire is wrapped around a soft iron nail, the resulting electromagnet will have a stronger magnetic field, thus improving its ability to pick up paper clips.

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The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively.

What is length?
Length is a concept used to describe the magnitude of a particular object or distance between two points. It is typically measured in units such as feet, inches, meters, miles, and kilometers. Length is often used to describe the size of an object and the distance between two points. Length can also be used to measure the time required to travel between two points. Length is a fundamental concept in mathematics, physics, and engineering.

The first dotted line shown at the top of the chart is 23.39.

b. With Overall Mean selected, what is the length of the second dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)

The second dotted line shown at the top of the chart is 23.28.

c. With Overall Mean selected, what is the length of the third dotted line shown at the top of the chart? (Hint: Use the Show Data button in the calculations window.) (Report two decimal places. Do not include a negative sign.)

The third dotted line shown at the top of the chart is 24.17.

Conclusion: The interactive tool provided a sample size of 41 and a plot of the Age variable. The three dotted lines shown at the top of the chart had lengths of 23.39, 23.28, and 24.17 respectively. This data can be used to analyze the age of respondents in Market Research.

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Belinda will need to invest $290,109.79 in the CD to earn a yearly income of $35,000 for 10 years.

The annual rate of interest that is charged on a loan or generated on an investment is known as the APR (Annual Percentage Rate), and it is stated as a percentage. Compounding, which is the practise of adding interest to the principal amount of a loan or investment, is not taken into account.

On the other hand, APY (Annual Percentage Yield) does consider the impacts of compounding. The annual percentage yield, or APY, is the rate of return that an investor receives on an investment over the course of a year. Both the interest gained on the initial sum and the interest earned on any prior interest that has been reinvested are considered.

The compound interest is given by the formula:

[tex]A = P * (1 + r/n)^{(n*t)}[/tex]

Now, isolating the value of P we have:

[tex]P = A / (1 + r/n)^{(n*t)}[/tex]

Now, substituting the value we have:

[tex]P = 35000 / (1 + 0.028/1)^{(1*10)} = $290,109.79[/tex]

Hence, Belinda will need to invest $290,109.79 in the CD to earn a yearly income of $35,000 for 10 years.

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We know that the plane flew at each speed which is at 100mph and 110mph for 3 hours each.

Speed is what it means. The rate at which the location of an object shifts in any direction.

Speed is defined as the ratio of the distance traveled to the time required to cover that distance.

Speed is a scalar quantity since it just has a direction and no magnitude.

The distance an object covers in a given amount of time is known as

speed.

The SI unit of speed is m/s or meters per second.

It has a scalar value.

Speed=Distance/Time.

So, using the speed:

Total miles = 630 in 6 hours.

Then,

100*3=300

110*3=330

Now,

300 + 330 = 630 miles

Therefore, we know that the plane flew at each speed which is at 100mph and 110mph for 3 hours each.

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The equation of the hyperbola with centered at the origin has vertices at ( ±√7 , 0) and foci at (±√27 , 0) is (x²/7) - (y²/20) = 1.

The equation of a hyperbola centered at the origin with vertices on the x-axis is, (x²/a²)-(y²/b²) = 1.

The asymptotes' distance is b, while the distance between the origin and vertex is a. In this case, a = √7 and c = √27, distance from the origin to a focus is c. We can use the relationship a² + b² = c² to solve for b:

b² = c² - a² = 27 - 7 = 20

So, we get, the equation of the hyperbola to be,

(x²/7) - (y²/20) = 1.

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A hyperbola centered at the origin has vertices at ( ±√7 , 0) and foci at (±√27 , 0). Write the equation of this hyperbola.

Answer: 7.5 ft

Step-by-step explanation:

W x L = 16 x 30 = 480

V / (W x L) = H = 3600 / 480 = 7.5 ft

The Coordinates of B (0, -2), C(0, -1) and D(-2, -1).

We have, the vertices of quadrilateral of A(1, -2).

Since AB = -1 which means that B is located 1 unit left then coordinates of B are

= (1 -1 , -2)

= (0, -2)

Now, C must have the same y coordinate as B. Also CB is vertical length 1 which moved above by 1 unit the coordinates of C

C (0, -2+1) = (0, -1)

and the coordinates of D are (0 -2, -1) = (-2, -1)

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The surface area of the given right rectangular prism will be 592 square inches.

The formula for a right rectangular prism's surface area is:

SA = 2lh + 2lw + 2lh

where l denotes the prism's length, w its width, and h its height.

Here, l is equal to 12 feet, w to 8 feet, and h to 10 feet. When these values are added to the formula, we obtain:

SA = 2(12)(8) + 2(12)(10) + 2(8)(10) (10)

SA = 192 + 240 + 160

SA = 592

Hence, the right rectangular prism has a surface area of 592 square feet.

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It would be 360 ft shorter to walk along the diagonal path from A to C rather than walking along the edge of the park from A to C.

To find out how much shorter it would be to walk along the diagonal path from A to C, we need to compare the lengths of the two paths: the diagonal path and the path along the edge of the park.

First, we can use the Pythagorean theorem to find the length of the diagonal path. In the rectangle ABCD, diagonal AC is the hypotenuse of a right triangle with sides AB and BC. So:

AC² = AB² + BC²

AC² = (720 ft)² + (540 ft)²

AC² = 518400 + 291600

AC² = 810000

AC = √810000

AC = 900 ft

So the length of the diagonal path from A to C is 900 ft.

Next, we can find the length of the path along the edge of the park from A to C. This path consists of two sides of the rectangle: AB and BC. So:

Length of path from A to C = AB + BC

Length of path from A to C = 720 ft + 540 ft

Length of path from A to C = 1260 ft

So the length of the path along the edge of the park from A to C is 1260 ft.

To find out how much shorter it would be to walk along the diagonal path, we can subtract the length of the diagonal path from the length of the path along the edge of the park:

1260 ft - 900 ft = 360 ft

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The average velocity for 0.5 seconds: -11 ft/s

The average velocity for 0.1 seconds is -33.6 ft/s

The average velocity for 0.05 seconds: -34 ft/s

The average velocity for 0.01 seconds : -16 fts

change in position using the height function y = 50t - 16t² for the given time intervals.

(i) 0.5 seconds:

y(2) = 50(2) - 16(2²) = 100 - 64 = 36 ft

y(2.5) = 50(2.5) - 16(2.5²) = 125 - 100 = 25 ft

Average velocity = (25 - 36) / 0.5 = -11 ft/s

(ii) 0.1 seconds:

y(2) = 36 ft (calculated before)

y(2.1) = 50(2.1) - 16(2.1²) ≈ 32.64 ft

Average velocity = (32.64 - 36) / 0.1 = -33.6 ft/s

(iii) 0.05 seconds:

y(2) = 36 ft (calculated before)

y(2.05) = 50(2.05) - 16(2.05²) ≈ 34.32 ft

Average velocity = (34.32 - 36) / 0.05 = -34 ft/s

(iv) 0.01 seconds:

y(2) = 36 ft (calculated before)

y(2.01) = 50(2.01) - 16(2.01²) ≈ 35.84 ft

Average velocity = (35.84 - 36) / 0.01 = -16 ft/s

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The total number of fluid ounces contained in 1 large glass of iced tea is 20 ounces

From the question, we are to calculate the total number of fluid ounces contained in 1 large glass of iced tea

Let the number of fluid ounces contained in 1 small glass be x

and

The number of fluid ounces contained in 1 large glass be y

Thus,

From the statement

"1 small glass and 2 large glasses contain a total of 48 fluid ounces of iced tea

2 small glasses and 3 large glasses contain a total of 76 fluid ounces of iced tea"

We can write that

x + 2y = 48

and

2x + 3y = 76

Now, we will solve the equations simultaneously

From the first equation,

x + 2y = 48

We can write that

x = 48 - 2y

Substitute into the second equation

2x + 3y = 76

2(48 - 2y) + 3y = 76

96 - 4y + 3y =76

96 - y = 76

96 - 76 = y

20 = y

Therefore,

y = 20

Hence, the number of fluid ounces in 1 large glass is 20 ounces

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Answer:

y=-6x+-4

Step-by-step explanation:

hi

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{0}) \implies y +4 = - 6 ( x -0) \\\\\\ y+4=-6x\implies {\Large \begin{array}{llll} y=-6x-4 \end{array}}[/tex]