Question

problem 11: match the following equations with its graph and then identify the slope and the y-intercept.
1 $y=2x+1$
2 $y=\frac{1}{3}x-2$
3 $y=-\frac{2}{3}x+1$
a.
b.
c.

Explanation:

Step1: Recall slope-intercept form

Linear equations follow $y=mx+b$, where $m$ is slope, $b$ is y-intercept.

Step2: Analyze Equation 1: $y=2x+1$

Slope $m=2$ (positive, steep), y-intercept $b=1$. Matches Graph B.

Step3: Analyze Equation 2: $y=\frac{1}{3}x-2$

Slope $m=\frac{1}{3}$ (positive, gentle), y-intercept $b=-2$. Matches Graph A.

Step4: Analyze Equation 3: $y=-\frac{2}{3}x+1$

Slope $m=-\frac{2}{3}$ (negative), y-intercept $b=1$. Matches Graph C.

Answer:

1. Equation $y=2x+1$ matches Graph B: Slope = $2$, y-intercept = $(0, 1)$
2. Equation $y=\frac{1}{3}x-2$ matches Graph A: Slope = $\frac{1}{3}$, y-intercept = $(0, -2)$
3. Equation $y=-\frac{2}{3}x+1$ matches Graph C: Slope = $-\frac{2}{3}$, y-intercept = $(0, 1)$