What is the equation of the line perpendicular to the line with equation y=3/4x -1 and passing through the point (-3,5)

Question

What is the equation of the line perpendicular to the line with equation y=3/4x -1 and passing through the point (-3,5)

Answer 1

If a line has the equation y=rx+c, then its slope is r. The line perpendicular to it has slope -1/r so the equation of the perpendicular line looks like y=-x/r+k for some k. Since (-3,5) lies on the line, to find out what k is plug in x=-3 and y=5 into the new equation.

Answer 2

There are two things you need to find to write the equation of the line: slope and y-intercept.

Slope:

Perpendicular lines have opposite reciprocal slopes, so take the slope of the original equation (m in y=mx+b) and flip it upside down and change the sign (positive to negative, or negative to positive). Then write a new equation, y=mx+b, where only the m is replaced with the new slope you found.

y-intercept:

Then plug in the x and y coordinates from the point your line is supposed to pass through into this new equation. Solve for b, which should be the only missing variable. Once you know what b is, you can write your final equation (y=mx+b) where y and x are written as variables, but you plug in the numbers you found for m and b.

I hope that helps!