Question

Which equation best represents the graph (image is attached) A: y= -3/2xB: y=3/2xC: y= -2/3xD: y= 2/3x

Answer 1

To solve the exercise you can first find the slope of the line using this formula

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\Rightarrow\text{ Slope formula} \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}$

In this case, for example, you can take the points (-3,2) and (0,0). So, you have

$\begin{gathered} (x_1,y_1)=(-3,2) \\ (x_2,y_2)=(0,0) \\ m=\frac{0-2}{0-(-3)} \\ m=\frac{0-2}{0+3} \\ m=-\frac{2}{3} \end{gathered}$

Now, you can use the point-slope formula and solve for y. The point-slope formula is

$y-y_1=m(x-x_1)$

So, you have

$\begin{gathered} y-2=-\frac{2}{3}(x-(-3)) \\ y-2=-\frac{2}{3}(x+3) \\ \text{ Apply the distributive property to the right side of the equation} \\ y-2=-\frac{2}{3}\cdot x-\frac{2}{3}\cdot3 \\ y-2=-\frac{2}{3}x-2 \\ \text{ Add 2 from both sides of the equation} \\ y-2+2=-\frac{2}{3}x-2+2 \\ y=-\frac{2}{3}x \end{gathered}$

Therefore, the equation that best represents the graph is

$c\colon y=-\frac{2}{3}x$