Answer:
[tex]y = - \frac{1}{3} x - 4[/tex]
Step-by-step explanation:
The equation of a kind can be written in the slope intercept form, y= mx +c, where m is the gradient and c is the y-intercept.
[tex]\boxed{gradient = \frac{y1 - y2}{x1- x2} }[/tex]
[tex]m = \frac{ - 2 - ( - 3)}{ - 6 - ( - 3)} [/tex]
[tex]m = \frac{ - 2 + 3}{ - 6 + 3}[/tex]
[tex]m = \frac{ 1}{ - 3} [/tex]
Substitute the value of m into the equation:
[tex]y = - \frac{1}{3} x + c[/tex]
To find the value of c, substitute a pair of coordinates.
When x= -3, y= -3,
[tex] - 3 = - \frac{1}{3} ( - 3) + c[/tex]
[tex] - 3 = 1 + c[/tex]
c= -3 -1
c= -4
∴ The equation of the line is [tex]y = - \frac{1}{3} x -4[/tex].
