Question

which graph represents a line with a slope of $-\frac{2}{3}$ and a y - intercept equal to that of the line $y = \frac{2}{3}x - 2$?

Explanation:

Step1: Identify target y-intercept

The line $y=\frac{2}{3}x-2$ uses slope-intercept form $y=mx+b$, where $b$ is the y-intercept. So the target y-intercept is $b=-2$.

Step2: Identify target slope

The required slope is $m=-\frac{2}{3}$, meaning the line decreases 2 units vertically for every 3 units it moves horizontally right.

Step3: Match to graph

Check each graph:

• First graph: Slope positive, y-intercept -2 (wrong slope)
• Second graph: Slope positive, y-intercept 2 (wrong both)
• Third graph: Slope negative, y-intercept 2 (wrong intercept)
• Fourth graph: Slope $-\frac{2}{3}$ (down 2, right 3), y-intercept -2 (matches both)

Answer:

The bottom-most (fourth) graph, which has a negative slope of $-\frac{2}{3}$ and crosses the y-axis at $(0, -2)$