Question

question 5 of 10
what is the equation of the following line? be sure to scroll down first to see
all answer options.

a. $y = -\frac{1}{9}x$
b. $y = -3x$
c. $y = 9x$
d. $y = -\frac{1}{3}x$
e. $y = -9x$
f. $y = 3x$

Explanation:

Step1: Recall the 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 origin \((0,0)\), so when \( x = 0 \), \( y=0 \). Substituting into \( y=mx + b \), we get \( 0=m(0)+b \), which means \( b = 0 \). So the equation of the line is of the form \( y=mx \).

Step2: Calculate the slope \( m \)

The slope \( m \) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). We know the line passes through \((0,0)\) and \((- 3,9)\). Let \( (x_1,y_1)=(0,0) \) and \( (x_2,y_2)=(-3,9) \). Then \( m=\frac{9 - 0}{-3-0}=\frac{9}{-3}=- 3 \).

Step3: Write the equation of the line

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

Answer:

B. \( y = -3x \)