What is the intersection point of the line $y = 2x + 5$ and the line perpendicular to it that passes through the point $(5, 5)$?

Guest Jul 13, 2019

#1**+2 **

y = 2x + 5

In the form y = mx + b.....the slope = m = 2

And the slope of a perpendicular line = -1 /m = -1 /2

So...the equation of the perp line passing through (5,5) is

y = (-1/2) (x - 5) + 5

y = (-1/2)x + 5/2 + 10/2

y = (-1/2)x + 15/2

So....to find the intersection point.....set the y's equal

2x + 5 = (-1/2)x + 15/2

(5/2)x = 15/2 - 10/2

(5/2)x = 5/2 ⇒ x = 1

And y = 2(1) + 5 = 7

So...the intersection point is (1,7)

Here's a graph : https://www.desmos.com/calculator/qk27oulorw

CPhill Jul 13, 2019