Question

which description of the graph of the linear inequality ( y > 3x - 8 ) is correct?

• the graph will be a dashed line with a ( y )-intercept of negative eight and a slope of three. the graph will be shaded below the line.
• the graph will be a solid line with a ( y )-intercept of three and a slope of negative eight. the graph will be shaded above the line.
• the graph will be a solid line with a ( y )-intercept of three and a slope of negative eight. the graph will be shaded below the line.
• the graph will be a dashed line with a ( y )-intercept of negative eight and a slope of three. the graph will be shaded above the line.

Explanation:

1. For linear inequalities, use a dashed line when the symbol is $>$ or $<$ (since the line itself is not part of the solution). Here, the inequality is $y > 3x - 8$, so the line is dashed.
2. The equation $y=3x-8$ is in slope-intercept form $y=mx+b$, where $m$ (slope) is 3 and $b$ (y-intercept) is $-8$.
3. For inequalities with $y > \text{[linear expression]}$, the region above the line is shaded, as all points there will have $y$-values greater than the value of the line at that $x$.

Answer:

The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line.