Question

select the correct answer.
which equation describes the line graphed above?
a. $y = \frac{3}{2}x - 6$
b. $y = \frac{2}{3}x - 6$
c. $y = \frac{3}{2}x + 4$
d. $y = \frac{2}{3}x + 4$

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at (0, 4), so the y-intercept \( b = 4 \). This eliminates options A and B which have \( b = -6 \).

Step2: Calculate the slope

Use two points on the line, e.g., (-6, 0) and (0, 4). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 0}{0 - (-6)}=\frac{4}{6}=\frac{2}{3} \).

Step3: Write the equation

The slope-intercept form is \( y = mx + b \). With \( m=\frac{2}{3} \) and \( b = 4 \), the equation is \( y=\frac{2}{3}x + 4 \).

Answer:

D. \( y = \frac{2}{3}x + 4 \)