Question

question 3 of 10
what is the equation of the following line? be sure to scroll down first to see
all answer options.

a. ( y = -\frac{2}{3}x )
b. ( y = 2x )
c. ( y = 3x )
d. ( y = -\frac{3}{2}x )
e. ( y = \frac{3}{2}x )
f. ( y = \frac{2}{3}x )

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify points

The line passes through \((0, 0)\) and \((-2, -3)\). Let \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(-2, -3)\).

Step3: Calculate slope

Substitute into the slope formula: \( m=\frac{-3 - 0}{-2 - 0}=\frac{-3}{-2}=\frac{3}{2} \).

Step4: Determine equation

Since the line passes through the origin \((0,0)\), its equation is in the form \( y = mx \), where \( m=\frac{3}{2} \). So the equation is \( y=\frac{3}{2}x \).

Answer:

E. \( y = \frac{3}{2}x \)