Question

which graph has a slope -4/5 and y intercept of -4?

Explanation:

Step1: Recall slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m=-\frac{4}{5}$ and $b = - 4$.

Step2: Analyze slope

A negative slope means the line is decreasing from left to right. So we can rule out graphs with positive - sloped lines (graphs A and C which have upward - sloping lines).

Step3: Analyze y - intercept

The y - intercept is the point where the line crosses the y - axis. Here, $b=-4$, so the line should cross the y - axis at the point $(0, - 4)$. Graph B crosses the y - axis at a positive value, while graph D crosses the y - axis at a negative value close to - 4 and is a decreasing line.

Answer:

D