Question

3. What is the equation of the line perpendicular to that passes through ? Write your answer in slope-intercept form. Show your work.

Answer 1

It looks like some information is missing from your question (the equation of the given line and the coordinates of the point). Could you provide those?

Meanwhile, here is the general method and a quick example so you can see the steps.

General steps
1. Put the given line into slope-intercept form y = mx + b (solve for y) and read off its slope m.
2. The slope of a perpendicular line is m_perp = −1/m (unless the given line is vertical, in which case the perpendicular is horizontal with slope 0; or the given line is horizontal, in which case the perpendicular is vertical — you would then give an equation x = constant).
3. Use point-slope form with the perpendicular slope and the given point (x1,y1):
y − y1 = m_perp (x − x1).
4. Rearrange to slope-intercept form y = m_perp x + b by solving for y and simplifying; b = y1 − m_perp x1.

Example
Given line: y = 2x + 3, and point (4, 1).
1. Slope of given line m = 2.
2. Perpendicular slope m_perp = −1/2.
3. Point-slope: y − 1 = (−1/2)(x − 4).
4. Expand: y − 1 = (−1/2)x + 2 → y = (−1/2)x + 3.

So the perpendicular line through (4,1) is y = (−1/2)x + 3.

If you send the specific line and point from your problem, I’ll compute that exact perpendicular line and show the work.