Answer:
The required inequality is \(\frac{y}{7}\leq \frac{x}{3}+2\).
Step-by-step explanation:
From the given graph it is clear that the related line passing throguh the points (-6,0) and (0,14).
If a line passing through two points, then the equation of line is
\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)
The equation of related line is
\(y-0=\frac{14-0}{0+6}(x+6)\)
\(y=\frac{14}{6}(x+6)\)
\(y=\frac{7}{3}(x+6)\)
Divide both sides by 7.
\(\frac{1}{7}y=\frac{1}{3}(x+6)\)
\(\frac{y}{7}=\frac{x}{3}+2\)
The equation of related line is \(\frac{y}{7}=\frac{x}{3}+2\).
The relates line is solid line and the shaded region is below the line therefore the sides of inequality is ≤.
Therefore the required inequality is \(\frac{y}{7}\leq \frac{x}{3}+2\).
