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

Explanation:

Step1: Rewrite the inequality in slope - intercept form

First, solve $6x + 2y>-10$ for $y$. Subtract $6x$ from both sides: $2y>-6x - 10$. Then divide by 2: $y>-3x - 5$.

Step2: Analyze the boundary line

The boundary line of the inequality $y>-3x - 5$ is $y = - 3x-5$. The slope $m=-3$ and the y - intercept $b = - 5$. Since the inequality is $y>-3x - 5$ (not $y\geq - 3x - 5$), the boundary line is dashed.

Step3: Test a point

Choose a test - point not on the line, say $(0,0)$. Substitute $x = 0$ and $y = 0$ into the inequality $y>-3x - 5$. We get $0>-3(0)-5$, or $0>-5$, which is true. So, the region that contains the point $(0,0)$ is the solution region.

The graph with a dashed line $y=-3x - 5$ and the region above the line (including the region that contains the origin $(0,0)$) is the correct graph. Without specific labels for the graphs, we can't identify it by name, but the correct graph has a dashed line with a slope of - 3 and y - intercept of - 5 and the shaded region above the line.