Question

graph the linear inequality below.
$y < 2x + 5$
show your work here

Explanation:

Step1: Identify boundary line

The boundary is $y=2x+5$, slope $m=2$, y-intercept $b=5$.

Step2: Plot boundary line

Use dashed line (since $y<$, not $\leq$). Plot points: when $x=0$, $y=5$; $x=2$, $y=9$; $x=-3$, $y=-1$. Connect with dashed line.

Step3: Test a point for shading

Test $(0,0)$: $0 < 2(0)+5$ → $0<5$, which is true.

Step4: Shade correct region

Shade the area below the dashed line (since the test point in this region satisfies the inequality).

Answer:

The graph has a dashed line for $y=2x+5$, with the region below this line shaded.