Question

(-6,8); perpendicular to y = -3/2x -1

Answer 1

`y = (2)/(3) x + 12`

Explanation:

`y = - (3)/(2) x - 1`

The gradient of a line is the coefficient of x when the equation of the line is written in the form of y=mx+c.

Thus, gradient of given line=
`- (3)/(2)`.

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

(Gradient of line)(-3/2)= -1

Gradient of line

`- 1 / ( - (3)/(2) ) \\ = - 1( - (2)/(3) ) \\ = (2)/(3)`

Substitute m=
`(2)/(3)` into y=mx+c:

`y = (2)/(3) x + c`

To find the value of c, substitute a pair of coordinates.

When x= -6, y= 8,

`8 = (2)/(3) ( - 6) + c \\ \\ 8 = - 4 + c \\ c = 8 + 4 \\ c = 12`

Thus, the equation of the line is
`y = (2)/(3) x + 12`.