Question

on a piece of paper, graph $y - 3 > 2x + 2$. then determine which answer choice matches the graph you drew.
a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Step1: Simplify the inequality

Rearrange to isolate $y$:
$y - 3 > 2x + 2$
$y > 2x + 5$

Step2: Identify line properties

The boundary line is $y=2x+5$, which has a y-intercept $(0,5)$ and slope $2$. Since the inequality is $>$, the line is dashed (not included in the solution).

Step3: Test a point for shading

Use $(0,0)$: $0 > 2(0)+5$ → $0>5$, which is false. So we shade the region not containing $(0,0)$ (above the line).

Step4: Match to graph

A dashed line $y=2x+5$ with shading above the line corresponds to Graph A.

Answer:

A. Graph A