Question

What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?

y = –x + 33
y = –x + 36
y = 4x − 16
y = 4x + 16

Answer 1

y=4x+16

Explanation:

Let us first rearrange the equation of the given line to be in the form y=mx+c. M gives the gradient of the line and c gives the y intercept.

y-1=4(x+3)

y-1=4x+12

y=4x+13

The gradient of parallel lines is equal. For the second line m=4

m=Δy/Δx

(y-32)/(x-4)=4

y-32=4(x-4)

y-32=4x-16

y= 4x+16

The equation of line 2 will be y=4x+16

Answer 2

Hello!

The answer is:

The line that is parallel to the given line and passes through the point (4,32) is:

`y=4x+16`

Why?

To solve the problem, we need to remember that parallel lines have the same slope, so, we need to find a line that has the same slope that the given line and it also pass through the point (4,32).

So, we are given the line:

`y-1=4(x+3)\\\\y=4x+12+1\\\\y=4x+13`

So, we have that the line has a slope which is equal to "4".

Now, we have to find which of the given lines that have a slope equal to "4", also pass through the point (4,32), so, we need to evaluate it into the equations.

Therefore, evaluating we have:

Third line:

`y=4x-16\\\\32=4*4-16=0\\32=0`

We can see that the equation is not satisfied, so the line does not pass through the point.

So, evaluating the fourth line, we have:

`y=4x+16\\\\32=4*4+16=16+16=32\\\\32=32`

We can see that the equation is satisfied, so the line does pass through the point (4,32)

Hence, we have that the line that is parallel to the given line and passes through the point (4,32) is:

`y=4x+16`

Have a nice day!