Question

which of the lines graphed has a slope of -2 and a y - intercept of 3?

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 $m=-2$ and $b = 3$, the equation of the line is $y=-2x + 3$.

Step2: Analyze slope

A slope of $m=-2$ means for every 1 unit increase in $x$, $y$ decreases by 2 units. A negative slope indicates the line is decreasing from left to right.

Step3: Analyze y - intercept

The y - intercept $b = 3$ means the line crosses the y - axis at the point $(0,3)$.

Answer:

We look for a line that crosses the y - axis at $(0,3)$ and is decreasing with a relatively steep slope. Option B has a line that crosses the y - axis at 3 and has a negative slope. So the answer is B.