Question

question 4 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= (1/4)x
b. y=2x
c. y= - (1/2)x
d. y=4x
e. y= (1/2)x
f. y=-2x

Explanation:

Step1: Recall slope-intercept form

The equation of a line in slope - intercept form is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.
From the graph, we can see that the line passes through the point \( (0,0) \), so the y - intercept \( b = 0 \). So the equation of the line is of the form \( y=mx \).

Step2: Calculate the slope

The slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). We can use the points \( (x_1,y_1)=(0,0) \) and \( (x_2,y_2)=(- 4,8) \).
Substitute these values into the slope formula: \( m=\frac{8 - 0}{-4-0}=\frac{8}{-4}=-2 \).

Step3: Write the equation of the line

Since \( m=-2 \) and \( b = 0 \), the equation of the line is \( y=-2x \).

Answer:

F. \( y = -2x \)