Answer:
\(\textsf{F)}\quad y=\dfrac{3}{2}x\)
Step-by-step explanation:
To find the equation of the graphed line, start by determining its slope. This can be done by substituting the coordinates of the two given points into the slope formula:
\(\boxed{\begin{array}{l}\underline{\textsf{Slope formula}}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\textsf{where:}\\\phantom{w}\bullet\;\;m\; \textsf{is the slope.}\\\phantom{w}\bullet\;\;(x_1,y_1)\;\textsf{and}\;(x_2,y_2)\;\textsf{are two points on the line.}\end{array}}\)
In this case:
- (x₁, y₁) = (-2, -3)
- (x₂, y₂) = (0, 0)
Substitute the coordinates of the two points into the slope formula:
\(m=\dfrac{0-(-3)}{0-(-2)}=\dfrac{0+3}{0+2}=\dfrac{3}{2}\)
Now, substitute the slope m = 3/2 and point (-2, -3) into the point-slope formula:
\(y-y_1=m(x-x_1)\\\\\\y-(-3)=\dfrac{3}{2}(x-(-2))\\\\\\y+3=\dfrac{3}{2}x+3\\\\\\y=\dfrac{3}{2}x\)
Therefore, the equation of the graphed line is:
\(\Large\boxed{\boxed{y=\dfrac{3}{2}x}}\)
