Question

identify the graph of the function;
y = -\frac{2}{3}x + 5

Explanation:

Step1: Identify slope and y-intercept

The function $y = -\frac{2}{3}x + 5$ is in slope-intercept form $y=mx+b$, where $m=-\frac{2}{3}$ (negative slope, line falls left to right) and $b=5$ (y-intercept at $(0,5)$).

Step2: Analyze graph options

• First graph: Steep negative slope, does not match $m=-\frac{2}{3}$.
• Second graph: Gentle negative slope, crosses y-axis at 5, matches $m=-\frac{2}{3}$ and $b=5$.
• Third graph: Positive slope, contradicts negative $m$.
• Fourth graph: Positive slope, contradicts negative $m$.

Answer:

The correct graph is the second one (top row, right of the checked incorrect graph): a line with a gentle downward slope crossing the y-axis at 5.