Write the slope-intercept form of the equation of each line through a given point and parallel/perpendicular to a specific line. through (2, 3) and parallel to y = 4x - 1

Answer 1

Hello Delanie!

For this question based off what I'm understanding.

Since they are requesting a parallel line to the given line: y = 4x-1

For a line to be parallel to y = 4x-1, the line must have the same slope.

For y = 4x-1, the slope is 4 (m = 4).

Now, we can assemble our line that specifically passes through (2,3) with slope (m = 4) since we want to keep it parallel to our given line.

Using point slope form: (y - y0) = m(x-x0) where (x0,y0) = (2,3) and m = 4.

We have....

(y - 3) = 4*(x - 2)

Putting in (x0,y0) = (2,3) ensures that our line will pass through that specific point.

If you wanted to put it in slope intercept form, simply solve for 'y'

(y-3) = 4(x-2)

(y-3) = 4x - 8 by distribution of the 4 to (x-2)

y = 4x-8+3 by adding 3 to both sides to isolate 'y'

y = 4x-5

Hence,

our slope intercept for our line will be: y = 4x-5

But, you are welcome to keep it in point-slope form depending on what kind of simplification the question is asking for.

Hope this helps!