Answer:
[tex]y = \frac{2}{3} x + 12[/tex]
Step-by-step explanation:
[tex]y = - \frac{3}{2} x - 1[/tex]
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=[tex] - \frac{3}{2} [/tex].
The product of the gradients of perpendicular lines is -1.
(Gradient of line)(-3/2)= -1
Gradient of line
[tex]- 1 \div ( - \frac{3}{2} ) \\ = - 1( - \frac{2}{3} ) \\ = \frac{2}{3}[/tex]
Substitute m=[tex]\frac{2}{3} [/tex] into y=mx+c:
[tex]y = \frac{2}{3} x + c[/tex]
To find the value of c, substitute a pair of coordinates.
When x= -6, y= 8,
[tex]8 = \frac{2}{3} ( - 6) + c \\ \\ 8 = - 4 + c \\ c = 8 + 4 \\ c = 12[/tex]
Thus, the equation of the line is [tex]y = \frac{2}{3} x + 12[/tex].
