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

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 = -3x+4

For a line to be parallel to y = -3x+4, the line must have the same slope.

For y = -3x+4, the slope is -3 (m = -3).

Now, we can assemble our line that specifically passes through (-1,2) with slope (m = -3) since we want to keep it parallel to our given line.

Using point slope form: (y - y0) = m(x-x0) where (x0,y0) = (-1,2) and m = -3.

We have....

(y - 2) = -3*(x - (-1)) -> (y-2) = -3*(x+1)

Putting in (x0,y0) = (-1,2) 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-2) = -3(x+1)

(y-2) = -3x - 3 by distribution of the -3 to (x+1)

y = -3x-3+2 by adding 2 to both sides to isolate 'y'

y = -3x-1

Hence,

our slope intercept for our line will be: y = -3x-1

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!