Answer:
[tex]y=-\frac{12}{7}x-\frac{80}{7}[/tex]
Step-by-step explanation:
In order to find the slope-intercept form of a line when given two points, we need to first put it into point-slope form. The point-slope form is given by the equation:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and x₁ and y₁ is one of the two points.
Anyways, let's first find the slope. Let's designate (-2,-8) as x₁ and y₁ and (-9,4) as x₂ and y₂ (it doesn't really matter). The formula for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{(4)-(-8)}{(-9)-(-2)}=12/-7=-12/7[/tex]
So, the slope is -12/7.
Now, pick a point for the point-slope form. To keep things consistent, I'm going to use the point (-2,-8) as x₁ and y₁. Plug in -12/7 for m. Therefore:
[tex]y-(-8)=-\frac{12}{7}(x-(-2))\\[/tex]
Now, simplify, distribute, and isolate the y:
[tex]y+8=-\frac{12}{7}(x+2)\\y+8=-\frac{12}{7}x-\frac{24}{7}\\y=-\frac{12}{7}x-\frac{24}{7}-8\\y=-\frac{12}{7}x-\frac{24}{7}-\frac{56}{7} \\y=-\frac{12}{7}x-\frac{80}{7}\\y=-\frac{12}{7}x-\frac{80}{7}[/tex]
