Question

which equation matches the graph?
a. $y = -\frac{1}{4}x + 3$
b. $y = -4x + 3$
c. $y = -4x - 3$

Explanation:

Step1: Identify y-intercept

The graph crosses the y-axis at (0, 3), so the y-intercept \( b = 3 \). This eliminates option C (\( y = -4x - 3 \)) as its y-intercept is -3.

Step2: Calculate slope

Pick two points on the line, e.g., (0, 3) and (1, -1). Slope \( m = \frac{-1 - 3}{1 - 0} = -4 \).

Step3: Match equation

The slope-intercept form is \( y = mx + b \). With \( m = -4 \) and \( b = 3 \), the equation is \( y = -4x + 3 \), which is option B.

Answer:

B. \( y = -4x + 3 \)