Question

which description of the graph of the linear inequality ( y geq 7x - 4 ) is correct?

• 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 negative four and a slope of seven. the graph will be shaded above 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.
• 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.

Explanation:

Step1: Identify line type

For $y \geq 7x - 4$, the $\geq$ inequality uses a solid line (includes boundary).

Step2: Extract slope and intercept

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

Step3: Determine shading direction

$y \geq$ means shade above the line (all $y$ values greater than the line).

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.