Answer:
[tex]y=-\frac{8}{3}x-11[/tex]
Step-by-step explanation:
Given:
Two points on a line are given as:
(-6, 5) and (-3, -3)
Now, equation of a line with two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given as:
[tex]y-y_1=m(x-x_1)[/tex]
Where, 'm' is the slope and is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, plugging the value of 'm' in the above equation, we get:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Here, [tex](x_1,y_1)=(-6,5)\ and\ (x_2,y_2)=(-3,-3)[/tex]
[tex]y-5=(\frac{-3-5}{-3-(-6)})(x-(-6))\\\\y-5=(\frac{-8}{-3+6})(x+6)\\\\y-5=\frac{-8}{3}(x+6)\\\\y-5=-\frac{8}{3}x-16\\\\y=-\frac{8}{3}x-16+5\\\\y=-\frac{8}{3}x-11[/tex]
Therefore, the equation of a line passing through (-6,5) and (-3,-3) is:
[tex]y=-\frac{8}{3}x-11[/tex]
