Question

question 8 of 10
what is the equation of the following line? be sure to scroll down first to see
all answer options.

a. ( y = -3x )
b. ( y = \frac{1}{5}x )
c. ( y = -7x )
d. ( y = 7x )
e. ( y = 3x )
f. ( y = 21x )

Explanation:

Step1: Recall the slope - intercept form of a line

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.

Step2: Find the y - intercept (\( b \))

The line passes through the point \( (0,0) \). When \( x = 0 \), \( y=b \). So, substituting \( x = 0 \) and \( y = 0 \) into \( y=mx + b \), we get \( 0=m\times0 + b \), which implies \( b = 0 \). So the equation of the line is of the form \( y=mx \).

Step3: 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 that the line passes through \( (0,0) \) and \( (1,7) \). Let \( (x_1,y_1)=(0,0) \) and \( (x_2,y_2)=(1,7) \). Then \( m=\frac{7 - 0}{1 - 0}=\frac{7}{1}=7 \).

Step4: Write the equation of the line

Since \( m = 7 \) and \( b = 0 \), the equation of the line is \( y=7x \).

Answer:

D. \( y = 7x \)