What is the intersection point of the line $y = 2x + 5$ and the line perpendicular to it that passes through the point $(5, 5)$?
+128399 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
