Question

question 3 of 10 what is the equation of the following line? be sure to scroll down first to see all answer options. a. $y =-\frac{1}{3}x$ b. $y = 3x$ c. $y=-3x$ d. $y =-\frac{1}{9}x$ e. $y = 9x$ f. $y=-9x$

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Since the line passes through the origin $(0,0)$, $b = 0$, and the equation is $y=mx$.

Step2: Calculate the slope

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(- 3,9)$. So $m=\frac{9 - 0}{-3 - 0}=\frac{9}{-3}=-3$.

Step3: Write the equation

Substituting $m=-3$ into $y = mx$, we get $y=-3x$.

Answer:

C. $y = - 3x$