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

xplosions Jun 30, 2020

#1**-1 **

Equation of line: y = 2x + 5

Equation of perpendicuar line: y - 5 = 1/2(x - 5)

Intersection point: (-5/3, 5/3)

Guest Jun 30, 2020

#3**+2 **

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).**

gwenspooner85 Jun 30, 2020