To solve the exercise you can first find the slope of the line using this formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\Rightarrow\text{ Slope formula} \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]
In this case, for example, you can take the points (-3,2) and (0,0). So, you have
[tex]\begin{gathered} (x_1,y_1)=(-3,2) \\ (x_2,y_2)=(0,0) \\ m=\frac{0-2}{0-(-3)} \\ m=\frac{0-2}{0+3} \\ m=-\frac{2}{3} \end{gathered}[/tex]
Now, you can use the point-slope formula and solve for y. The point-slope formula is
[tex]y-y_1=m(x-x_1)[/tex]
So, you have
[tex]\begin{gathered} y-2=-\frac{2}{3}(x-(-3)) \\ y-2=-\frac{2}{3}(x+3) \\ \text{ Apply the distributive property to the right side of the equation} \\ y-2=-\frac{2}{3}\cdot x-\frac{2}{3}\cdot3 \\ y-2=-\frac{2}{3}x-2 \\ \text{ Add 2 from both sides of the equation} \\ y-2+2=-\frac{2}{3}x-2+2 \\ y=-\frac{2}{3}x \end{gathered}[/tex]
Therefore, the equation that best represents the graph is
[tex]c\colon y=-\frac{2}{3}x[/tex]
