Question

Write an equation in slope-intercept form for the line that passes through the given point (-1,-7) and is perpendicular to the graph of 3x + 12 y = -6.

Answer 1

y = 4x -3

Explanation:

When a reference line is given in (almost) standard form, I find it convenient to use that form for the perpendicular line, then rearrange as required.

Dividing the given equation by 3 gives ...

x +4y = -2

Swapping the x- and y-coefficients and negating the new y-coefficient gives a perpendicular line:

4x -y = constant

We can find the constant by substituting the given point values:

4x -y = 4(-1) -(-7) = 3

Solving this for y gives ...

y = 4x -3