Question

due tuesday by 11:59pm points 8 submitting an external tool attempts available dec 9 at 12am - jan 5, 2026 at 11:59pm an inequality is shown. 4x + 5y ≥ 10 which graph represents the solution set of the inequality?

Explanation:

Step1: Rewrite the inequality in slope - intercept form

We start with the inequality \(4x + 5y\geq10\). To get it in the form \(y = mx + b\) (slope - intercept form), we solve for \(y\).
Subtract \(4x\) from both sides: \(5y\geq - 4x+10\).
Then divide each term by 5: \(y\geq-\frac{4}{5}x + 2\).

Step2: Analyze the boundary line

The equation of the boundary line is \(y =-\frac{4}{5}x + 2\). The slope \(m =-\frac{4}{5}\) and the y - intercept \(b = 2\). Since the inequality is \(\geq\), the boundary line should be solid (not dashed).

Step3: Analyze the region to shade

To determine which side of the line to shade, we can use a test point. A common test point is \((0,0)\). Substitute \(x = 0\) and \(y = 0\) into the inequality \(4x+5y\geq10\):
\(4(0)+5(0)=0\), and \(0\geq10\) is false. So we shade the region that does not include the origin \((0,0)\).

Now, looking at the first graph (the one with the solid line \(y =-\frac{4}{5}x + 2\) and shading above the line, not including the origin - side check), the line has a y - intercept of 2, a slope of \(-\frac{4}{5}\) (going down 4 units and right 5 units), and the shading is on the side where \(y\geq-\frac{4}{5}x + 2\) (since \((0,0)\) is not in the shaded region).

Answer:

The first graph (the one with the line passing through \((0,2)\) and \((2.5,0)\) approximately, with a solid line and shading above the line)