Question

question 1 of 10 what is the equation of the following line? be sure to scroll down first to see all answer options. (-4,8) (0,0) a. y = -\frac{1}{2}x b. y = 2x c. y = \frac{1}{2}x d. y = -2x e. y = \frac{1}{4}x f. y = 4x

Explanation:

Step1: Find the slope formula

The slope $m$ of a line passing through 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 $(x_2,y_2)=(-4,8)$.

Step2: Calculate the slope

$m=\frac{8 - 0}{-4-0}=\frac{8}{-4}=- 2$.

Step3: Determine the equation of the line

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Since the line passes through the origin $(0,0)$, $b = 0$. So the equation is $y=-2x$.

Answer:

D. $y=-2x$