Question

question 5 of 10
what is the equation of the following line? be sure to scroll down first to see
all answer options.
(-3,9)
(0, 0)
a. y = -\frac{1}{9}x
b. y = -3x
c. y = 9x
d. y = -\frac{1}{3}x
e. y = -9x
f. y = 3x

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form 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 \((0,0)\), 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 have two points on the line: \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(- 3,9)\).
Substitute these values into the slope formula: \( m=\frac{9 - 0}{-3-0}=\frac{9}{-3}=- 3\).

Step3: Write the equation of the line

Since \( m=-3 \) and \( b = 0\), the equation of the line is \( y=-3x \).

Answer:

B. \( y = -3x \)