Question

find the equation of a line that goes through the point (2,-3) and is perpendicular to the line y= -2/5x+6

Answer 1

To get a perpendicular line to y=-2/5x+6 all you need to do is get the negative reciprocal of the slope then use (2,-3) and point slope formula to get your new equation.

y=-2/5x+6

m=-2/5 so new equation slope is m=5/2


y−b=m(x−a) or y-y1=m(x-x1)

point is (2,-3)

plug and chug

y-(-3)=5/2(x-2)
y=5/2x-8

Answer 2

Find the negative reciprocal of the given line's slope in order to determine what the slope of the line will be.

-2/5 -> -5/2 -> 5/2

Your line now looks like this: y = 5/2x + b

Now, substitute the given point into the y and x variables and solve for b.

y = 5/2x + b
-3 = 5/2(2) + b
-3 = 5 + b
-8 = b

You are now done. The line is y = 5/2x - 8.