Answer:
[tex]y = \frac{3}{2} x + 8[/tex]
Step-by-step explanation:
The given equation is written in the form of y=mx+c (where m is the gradient and c is the y-intercept).
Thus, gradient of given equation= -⅔
The products of the gradient of perpendicular lines is -1.
(Gradient of line)(-⅔)= -1
Gradient of line
[tex] = - 1 \div ( - \frac{2}{3} ) \\ = \frac{3}{2} [/tex]
Hence, m= [tex] \frac{3}{2} [/tex].
Subst. m= [tex] \frac{3}{2} [/tex]into the equation:
[tex]y = \frac{3}{2} x + c[/tex]
To find the value of c, substitute a pair of coordinates into the equation:
When x= -4, y= 2,
[tex]2 = \frac{3}{2} ( - 4) + c \\ 2 = - 6 + c \\ c = 2 + 6 \\ c = 8[/tex]
Thus, the equation of the line is [tex]y = \frac{3}{2} x + 8[/tex].
