Question

learning goal from lesson 3
s2 i can graph solutions to linear inequalities on a coordinate plane.
lesson reflection (circle one)
i got it! i’m still learning it.

1. graph the inequality. (1 point)

y ≤ 5x + 4

Explanation:

Step1: Plot boundary line

The inequality is $y \leq 5x + 4$. First, plot the boundary line $y = 5x + 4$. The y-intercept is $(0, 4)$ (when $x=0$, $y=4$). For another point, set $x=1$: $y=5(1)+4=9$, so $(1,9)$ is on the line. Draw a solid line (since $\leq$ includes equality).

Step2: Shade the region

Test the origin $(0,0)$: $0 \leq 5(0)+4 \Rightarrow 0 \leq 4$, which is true. Shade the area below the boundary line (where the test point lies).

Answer:

A solid line through $(0,4)$ and $(1,9)$, with shading below the line.