Answer:
[tex]y=\frac{2}{3}x-6[/tex]
Step-by-step explanation:
Use the slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept. Looking at the graph, you can find the y-intercept. The y-intercept is the point where x equals 0:
[tex]b=-6[/tex]
[tex]y-intercept=(0,-6)[/tex]
To find the slope, take any two points from the line:
[tex](6,-2)(3,-4)[/tex]
Use the slope formula for when you have two points:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]
The rise over run is the change in the y-axis over the change of the x-axis. Insert the appropriate values:
[tex](6(x_{1}),-2(y_{1})\\(3(x_{2}),-4(y_{2})[/tex]
[tex]\frac{-4-(-2)}{3-6}[/tex]
Simplify parentheses (two negatives makes a positive):
[tex]\frac{-4+2}{3-6}[/tex]
[tex]\frac{-2}{-3}[/tex]
Simplify (two negatives make a positive):
[tex]m=\frac{2}{3}[/tex]
The slope is [tex]\frac{2}{3}[/tex] and the y-intercept is [tex]-6[/tex]. Insert these into the equation:
[tex]y=\frac{2}{3}x-6[/tex]
Finito.
