Answer: Choice C
[tex]y \ge 4x-5[/tex]
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Explanation:
First we need to find the equation of the boundary line. This is the line that separates the shaded region versus the non-shaded region.
The boundary line goes through (0,-5) so this is the y intercept, so b = -5
Another point on the boundary line is (1,-1). The slope of the line through (0,-5) and (1,-1) is m = 4. You can use the slope = rise/run idea or you could use the slope formula to get m = 4.
With m = 4 and b = -5, the y = mx+b equation updates to y = 4x-5
The boundary line has the equation y = 4x-5
Because it is a solid boundary line (instead of dashed) and the shading is above the boundary, this means we change the equal sign to "greater than or equal to"
Therefore we get [tex]y \ge 4x-5[/tex]
Note: a solid boundary line means that points on this boundary are included in the solution set. A dashed boundary line would mean you don't include boundary points in the solution set. So that's why there is a "or equal to" portion in the inequality sign.
