Answer:
[tex]y=-\frac{1}{3}x -5[/tex]
Step-by-step explanation:
Slope-intercept form is [tex]y=mx+b[/tex], so that's the equation you'll be plugging your values into.
To find the slope of a line, you only need two points, which this graph gives you. (-6, -3) and (6, -7)
Slope, or m, can be found by using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Now you just plug in your points into the formula, giving you [tex]\frac{(-7)-(-3)}{(6)-(-6)} =\frac{-4}{12} =\frac{-1}{3}[/tex] .
Since you don't have an intercept, choose one of the two given points to plug into the equation [tex]y-y_1=m(x-x_1)[/tex] .
* It doesn't matter which point you use, both will give you a correct answer.
Let's use (-6, -3).
Since you now have a [tex]y_1, x_1,[/tex] and your [tex]m[/tex], all you need to do is plug them in.
[tex]y-y_1=m(x-x_1)\\y-(-3)=-\frac{1}{3}(x-(-6))\\y+3=-\frac{1}{3} (x+6)\\y+3=-\frac{1}{3} x-2\\y=-\frac{1}{3} x-5[/tex]
If you want, you can plug in points just to confirm that this is the right equation. The simplest way to find out is by making x=0, which gives you a y value of -5. You can see on the graph that the line passes through -5 on the y-axis when x=0, so the equation is valid.
