Answer:
Equation of graphed line is ![\mathbf{y=\frac{2}{3}x-3}](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D%5Cfrac%7B2%7D%7B3%7Dx-3%7D)
Step-by-step explanation:
We need to write the equation of the graphed line.
The equation will be in slope intercept form
where m is slope and b is y-intercept
We need to find slope and y-intercept.
Finding slope
Slope can be found using formula: ![Slope=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We will use points (0,-3) and (3,2)
Looking at the graph, we get ![x_1=0, y_1=-3, x_2=3, y_2=-1](https://tex.z-dn.net/?f=x_1%3D0%2C%20y_1%3D-3%2C%20x_2%3D3%2C%20y_2%3D-1)
Putting values in graph and finding slope
![Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-1-(-3)}{3-0} \\Slope=\frac{-1+3}{3} \\Slope=\frac{2}{3}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5CSlope%3D%5Cfrac%7B-1-%28-3%29%7D%7B3-0%7D%20%20%5C%5CSlope%3D%5Cfrac%7B-1%2B3%7D%7B3%7D%20%20%5C%5CSlope%3D%5Cfrac%7B2%7D%7B3%7D)
So, we get slope ![\mathbf{\frac{2}{3} }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7B2%7D%7B3%7D%20%20%7D)
Finding y-intercept
y-intercept can be found when x is zero.
So, looking at graph, when x =0, y=-3
So, y-intercept is -3
Equation of Line
So, equation of line having slope
and y-intercept b = -3
![y=mx+b\\y=\frac{2}{3}x-3](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D%5Cfrac%7B2%7D%7B3%7Dx-3)
So, Equation of graphed line is ![\mathbf{y=\frac{2}{3}x-3}](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D%5Cfrac%7B2%7D%7B3%7Dx-3%7D)