+107 What is the intersection point of the line y = 2x + 5 and the line perpendicular to it that passes through the point (5,5)?
Equation of line: y = 2x + 5
Equation of perpendicuar line: y - 5 = 1/2(x - 5)
Intersection point: (-5/3, 5/3)
+781 The line perpendicular to y=2x+5 must have the slope -1/2. We then have that the perpendicular line's equation is y=-1/2x+b. We plug in the given point (5, 5) to solve for b.
y=-1/2x+b
5=-1/2(5)+b
5=-5/2+b
b=15/2
So the equation of this line is y=-1/2x+15/2. To find the intersection point of it and y=2x+5, we set -1/2x+15/2 and 2x+5 to be equal to each other.
-1/2x+15/2=2x+5
5/2x=5/2
x=1
Plug this value into either of the equations for the lines we have. y=2x+5 will be easier to work with.
y=2x+5
y=2(1)+5
y=7
Therefore the intersection point is (1, 7).
