A line has this equation: 5y-x=20 write an equation for the perpendicular line that goes through (2,-2)

y= -5x+8

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

Let's rewrite the formula of the given line so it is in the form of y=mx+c, to find out its gradient.

5y-x=20

5y= x+20

(÷5 throughout)

Hence, the gradient of the given line is .

The product of the gradients of 2 perpendicular lines is-1.

Subst. m= -5 into the equation.

y= -5x +c

To find c, substitute a coordinate into the equation.

When x=2, y= -2,

-2 = -5(2) +c

-2= -10 +c

c= 10 -2

c= 8

Thus, the equation of the line is y= -5x +8.