Question

which is the graph of linear inequality $6x + 2y > -10$?

Explanation:

Step1: Rewrite inequality to slope-intercept form

Start with the given inequality:
$$6x + 2y > -10$$
Subtract $6x$ from both sides:
$$2y > -6x - 10$$
Divide all terms by 2:
$$y > -3x - 5$$

Step2: Identify line properties

The boundary line is $y = -3x - 5$, which has:

• Slope $m = -3$
• Y-intercept $b = -5$

Since the inequality is $>$, the boundary line is dashed, and we shade the region above the line.

Step3: Verify with a test point

Use the origin $(0,0)$ as a test point:
$$0 > -3(0) - 5$$
$$0 > -5$$
This is true, so the region containing $(0,0)$ (above the line) is shaded.

Answer:

The correct graph is the first option (top-left graph with dashed line $y=-3x-5$ and shading above/right of the line, containing the origin).