Answer:
\(\textsf{C)}\quad y=-\dfrac{1}{3}x\)
Step-by-step explanation:
To find the equation of the graphed line, begin by determining its slope. To do this, substitute the coordinates of the two points on the line 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) = (-3, 1)
- (x₂, y₂) = (0, 0)
Substitute the coordinates into the slope formula:
\(m=\dfrac{0-1}{0-(-3)}=\dfrac{-1}{0+3}=-\dfrac{1}{3}\)
Now, substitute the slope and point (-3, 1) into the point-slope formula:
\(y-y_1=m(x-x_1)\\\\\\y-1=-\dfrac{1}{3}(x-(-3))\\\\\\y-1=-\dfrac{1}{3}x-1\\\\\\y=-\dfrac{1}{3}x\)
Therefore, the equation of the graphed line is:
\(\Large\boxed{\boxed{y=-\dfrac{1}{3}x}}\)
