Question

which function is represented by the graph below?
$y = \frac{1}{2}x - 4$
$y = -4x + 2$
$y = -4x + \frac{1}{2}$
$y = 2x - 4$

Explanation:

Step1: Identify y-intercept

The graph crosses the y-axis at $(0, -4)$. In the slope-intercept form $y=mx+b$, $b=-4$. This eliminates options $y=-4x+2$ and $y=-4x+\frac{1}{2}$.

Step2: Calculate slope

Use two points on the line: $(0, -4)$ and $(2, 0)$. Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-4)}{2-0}=\frac{4}{2}=2$.

Step3: Match to function

With $m=2$ and $b=-4$, the function is $y=2x-4$.

Answer:

$y=2x-4$