Question

Which is the equation in slope-intercept form for the line that passes through (3, 7)

and is perpendicular to 3x - 5y = 8?

Answer 1

`y = - (5)/(3) x + 12`

Explanation:

First, rewrite the given equation in the form of y=mx+c.

m is the gradient while c is the y-intercept.

3x-5y=8

5y= 3x -8

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

Thus, the gradient of the given equation is ⅗.

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

(gradient of line)(⅗) = -1

gradient of line= -1 ÷⅗

gradient of line=
`- (5)/(3)`

`y = - (5)/(3) x + c`

To find the value of c, substitute a coordinate.

When x=3, y=7,

`7 = - (5)/(3) (3) + c`

7= -5 +c

c= 7+5

c= 12

Hence, the equation of the line is
`y = - (5)/(3) x + 12`.