Answer:
[tex]y-2=3(x-4)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given a line contains the point (4, 2).
We also know that the line is parallel to y= 3x - 7.
We want to write the equation of this line.
Parallel lines have the same slopes.
First, let's find the slope of y = 3x - 7.
3 is in the place of where m (the slope) is, so that means it is the slope of that line.
It is also the slope of the line whose equation we want to write.
The equation of the line can be written in three ways:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well. Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.
SolvingSubstitute 3 as m in [tex]y-y_1=m(x-x_1)[/tex].
[tex]y-y_1=3(x-x_1)[/tex]
Now, substitute 4 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].
[tex]y-2=3(x-4)[/tex]
Topic: parallel and perpendicular lines
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Find the term named in the problem and the explicit formula.
13) 18,14,10,6,
14) 30,0,-30,-60,
Find a₂₂
Find a₃₇
15) -34,-31,-28,-25,
Find a₂₃
The named terms in the sequence are a₂₂ = -66, a₃₇ = -1050 and a₂₃ = 32
How to determine the named term in the sequence?Sequence 1
From the question, we have the following sequence that can be used in our computation:
18,14,10,6,
In the above sequence, we can see that the 4 is subtracted from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = 18
d = -4
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 22nd term, we have
a₂₂ = 18 + (22 - 1) * -4
Evaluate
a₂₂ = -66
Sequence 2
Here, we have
30,0,-30,-60,
In the above sequence, we can see that the 30 is subtracted from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = 30
d = -30
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 37th term, we have
a₃₇ = 30 + (37 - 1) * -30
Evaluate
a₃₇ = -1050
Sequence 3
Here, we have
-34,-31,-28,-25,
In the above sequence, we can see that the 3 is added from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = -34
d = 3
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 23rd term, we have
a₂₃ = -34 + (23 - 1) * 3
Evaluate
a₂₃ = 32
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Anna is buying a house selling for $285,000. To obtain the mortgage, Anna is required to make a 15 % down payment. Anna obtains a 25 -year mortgage with an interest rate of 5 %. Click the icon to view the table of monthly payments.
a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
a) Determine the amount of the required down payment.
a) The amount of the required down payment is $42,750.
b) The mortgage amount after the down payment is $242,250.
c) The monthly payment for both principal and interest is $1,416.17.
What is the down payment?The down payment refers to the upfront cash payment made to reduce the cost of the home.
After deducting the down payment from the home price the result is the loan amount.
Monthly payments pay part of the loan amount the computed interest.
The monthly payments and the down payment can be determined with an online finance calculator.
Home Price = $285,000
Down Payment = 15%
Loan Term = 25 years
Interest Rate = 5%
Monthly Pay: $1,416.17
Loan Amount $242,250 ($285,000 - $42,750)
Down Payment = $42,750 ($285,000 x 15%)
Total of 300 Mortgage Payments = $424,851 ($1,416.17 x 300)
Total Interest = $182,601
Thus, after making a down payment of $42,750 cash, Anna will be making monthly payments of $1,416.17 for 300 months.
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