Answer:
[tex]y=-\frac{1}{3}x-5[/tex]
Step-by-step explanation:
Given:
The two points on the line are:
[tex](x_1,y_1)=(-6,-3)\\(x_2,y_2)=(6,-7)[/tex]
Now, for a line with two points on it, the slope of the line is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For the points [tex](x_1,y_1)=(-6,-3)\ and\ (x_2,y_2)=(6,-7)[/tex], slope is:
[tex]m=\frac{-7-(-3)}{6-(-6)}\\m=\frac{-7+3}{6+6}\\m=\frac{-4}{12}=-\frac{1}{3}[/tex]
Now, for a line with slope 'm' and a point [tex](x_1,y_1)[/tex] on it is given as:
[tex]y-y_1=m(x-x_1)[/tex]
Plug in all the values and determine the equation of the line. This gives,
[tex]y-(-3)=-\frac{1}{3}(x-(-6))\\\\y+3=-\frac{1}{3}(x+6)\\\\y+3=-\frac{1}{3}x-\frac{1}{3}\times 6\\\\y+3=-\frac{1}{3}x-2\\\\y=-\frac{1}{3}x-2-3\\\\y=-\frac{1}{3}x-5[/tex]
Therefore, the equation of the line is:
[tex]y=-\frac{1}{3}x-5[/tex]
