Question

graph the inequality.
5x + 2y ≤ -2

Explanation:

Step1: Rewrite the inequality in slope - intercept form

We start with the inequality \(5x + 2y\leq - 2\). To get it in the form \(y=mx + b\), we solve for \(y\).
Subtract \(5x\) from both sides: \(2y\leq - 5x-2\).
Then divide each term by 2: \(y\leq-\frac{5}{2}x - 1\).

Step2: Graph the boundary line

The boundary line is \(y =-\frac{5}{2}x - 1\). Since the inequality is \(\leq\), the boundary line should be a solid line (because the points on the line are included in the solution set).
To graph the line, we can find two points.

• When \(x = 0\), \(y=-\frac{5}{2}(0)-1=-1\). So the point \((0, - 1)\) is on the line.
• When \(x = 2\), \(y=-\frac{5}{2}(2)-1=-5 - 1=-6\). So the point \((2,-6)\) is on the line.

Plot these two points \((0, - 1)\) and \((2,-6)\) and draw a solid line through them.

Step3: Shade the region

Since the inequality is \(y\leq-\frac{5}{2}x - 1\), we shade the region below the boundary line. We can test a point not on the line, for example, the origin \((0,0)\).
Substitute \(x = 0\) and \(y = 0\) into the original inequality: \(5(0)+2(0)=0\leq - 2\)? No. So the origin is not in the solution set, and we shade the region that does not include the origin (the region below the line \(y =-\frac{5}{2}x - 1\)).

Answer:

1. First, graph the solid line \(y =-\frac{5}{2}x - 1\) using two points (e.g., \((0,-1)\) and \((2, - 6)\)).
2. Then shade the region below the line.