Question

How do you find the equation that is perpendicular to 2x-5y=20, passing through the point (7,-8)?

Answer 1

To find a perpendicular line you first need to see the equation in slope intercept form. To do that you need to solve for y. 

2x - 5y = 20 ---> subtract 2x from both sides
-5y = -2x + 20 ---> divide by -5
y = 2/5x - 4

Now that you have this, note that a perpendicular line has opposite and reciprocal slope. Since the slope in our equation is 2/5, that means the new line will have -5/2 slope. So we use the point given and the slope to find the y intercept. 

y = mx + b
-8 = -5/2(7) + b ---> multiply
-8 = -35/2 + b ---> add 35/2 to both sides
19/2 = b

Now use our new slope and new y intercept to write the new equation. 

y = -5/2x + 19/2