Question

What is the slope of any line perpendicular to the line passing through `(3,13)` and `(-8,17)`?

Answer 1

write the equation in the form y=mx + b using the points (3,13) and (-8,17)

Find the slope `(13-17)/(3+8) = -4/11`

Then find the y-intercept, plug in one of the points for (x,y)

`13= (-4/11)* (3)+b`

Simplify

`13= -12/11 +b`

Solve for b, add `12/11` to both sides to isolate b

`b=14 1/11`

Then you get the equation

`y=-4/11 x + 14 1/11`

To find a PERPENDICULAR equation

The the slope of the perpendicular equation is
Opposite Reciprocal of the original equation

So the original equation had a slope of `-4/11`

Find the opposite reciprocal of that slope to find the slope of the perpendicular equation

The new slope is: `11/4`

Then find b, by plugging in a given point so either (3,13) or (-8,17)

`17= (11/4)*(-8)+b`

Simplify

`17 = -22 +b`

Add 22 to both sides to isolate b

`b=39`

The Perpendicular Equation is: `y=11/4 x + 39`