Answer:
[tex]y= -\frac{2}{3}x-3[/tex]
Step-by-step explanation:
Slope-intercept form is in y = mx + b format. To write an equation with that formula, substitute the m and the b for real values.
1) First, find m, or the slope of the equation. Pick any two points from the graph and substitute their x and y values into the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. I chose the points (0, -3) and (-3, -1):
[tex]m = \frac{(-1)-(-3)}{(-3)-(0)} \\m = \frac{-1+3}{-3-0}\\m = -\frac{2}{3}[/tex]
Thus, the slope is [tex]-\frac{2}{3}[/tex].
2) Now, find b, or the y-intercept of the equation. The y-intercept of a line is the point at which the line intersect the y-axis. By reading the graph, we can see that the line intersects the y-axis at (0,-3), thus that is the y-intercept.
3) Now, substitute [tex]-\frac{2}{3}[/tex] for m and -3 for b into the y = mx + b formula:
[tex]y= -\frac{2}{3}x-3[/tex]
