Question

1. the boundary line on the graph represents the equation 5x + 2y = 6. write an inequality that is represented by the graph.

Explanation:

Step1: Rewrite the line - equation in slope - intercept form

The given boundary line equation is \(5x + 2y=6\). Solve for \(y\):
\[

$$\begin{align*} 2y&=- 5x + 6\\ y&=-\frac{5}{2}x + 3 \end{align*}$$

\]

Step2: Determine the inequality sign

Since the boundary line is dashed, the inequality is either \(y>-\frac{5}{2}x + 3\) or \(y<-\frac{5}{2}x + 3\). We can test a point not on the line, say \((0,0)\). Substitute \(x = 0\) and \(y = 0\) into the inequality.
The region containing \((0,0)\) is shaded. Substituting into \(y<-\frac{5}{2}x + 3\), we get \(0<3\) which is True.

Answer:

\(y<-\frac{5}{2}x + 3\)