Question

1. which equation best represents line m?

a ( y = -3x - 4 )
b ( y = -\frac{1}{3}x - 4 )
c ( y = \frac{1}{3}x - 4 )
d ( y = 3x - 4 )

Explanation:

Step1: Identify slope and y-intercept

The line equation is in slope-intercept form \( y = mx + b \), where \( b \) is the y-intercept and \( m \) is the slope. From the graph, the line crosses the y-axis at \( (0, -4) \), so \( b = -4 \). To find the slope, pick two points. Let's use \( (0, -4) \) and \( (3, -3) \) (or other points). The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using \( (0, -4) \) and \( (3, -3) \): \( m = \frac{-3 - (-4)}{3 - 0} = \frac{1}{3} \). The slope is positive \( \frac{1}{3} \), and y-intercept is -4.

Step2: Match with options

Option C is \( y = \frac{1}{3}x - 4 \), which has slope \( \frac{1}{3} \) and y-intercept -4, matching our findings.

Answer:

C. \( y = \frac{1}{3}x - 4 \)