Question

which description of the graph of the linear inequality $y \geq 7x - 4$ is correct? the graph will be a solid line with a $y$-intercept of negative four and a slope of seven. the graph will be shaded above the line. the graph will be a dashed line with a $y$-intercept of seven and a slope of negative four. the graph will be shaded above the line. the graph will be a dashed line with a $y$-intercept of negative four and a slope of seven. the graph will be shaded below the line. the graph will be a solid line with a $y$-intercept of seven and a slope of negative four. the graph will be shaded below the line.

Explanation:

Step1: Identify line type

The inequality uses $\geq$, so the boundary line is solid (includes points on the line).

Step2: Find slope and intercept

The inequality is in slope-intercept form $y=mx+b$, where $m=7$ (slope) and $b=-4$ (y-intercept).

Step3: Determine shaded region

For $y \geq mx+b$, shade the region above the line (all $y$-values greater than or equal to the line's values).

Step4: Match to options

Compare the above details to the given choices.

Answer:

The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.