Question

question 6 of 10
what is the equation of the following line? be sure to scroll down first to see
all answer options.
(0, 0)
(4, -3)
a. ( y = 3x )
b. ( y = -4x )
c. ( y = -3x )
d. ( y = -\frac{3}{4}x )
e. ( y = -\frac{4}{3}x )
f. ( y = \frac{1}{4}x )

Explanation:

Step1: Recall the 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.

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 \( b = 0 \).

Step3: Calculate the slope (\( m \))

The slope \( m \) between 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 have two points on the line: \( (0,0) \) (let \( (x_1,y_1)=(0,0) \)) and \( (4,-3) \) (let \( (x_2,y_2)=(4,-3) \)).
Using the slope formula: \( m=\frac{-3 - 0}{4 - 0}=\frac{-3}{4}=-\frac{3}{4} \).

Step4: Write the equation of the line

Since \( m = -\frac{3}{4} \) and \( b = 0 \), the equation of the line in slope - intercept form is \( y=-\frac{3}{4}x+0 \), or simply \( y = -\frac{3}{4}x \).

Answer:

D. \( y = -\frac{3}{4}x \)