Chapter 6.5, Problem 5P

To determine

To calculate: inequality with the help of graph.

Answer to Problem 5P

  $\frac{1}{3}x-y<2$ or $x-3y<6$

Explanation of Solution

Given information:You are writing an inequality from a graph. The boundary line is dashed and has slope $\frac{1}{3}$ and $y-$ intercept $-2$ . The area above the line is shaded.

Calculation:

Equation of given line is, $y=mx+c=\frac{1}{3}x-2$ and the area above the line is shaded. Given situation is graphed as below,

  

In a standard form, equation of line is, $\frac{1}{3}x-y=2$

Now, for the area above the line, origin is there, which follows the inequality $\frac{1}{3}x-y<2$

As the boundary line is dashed there will be $<$ in the equation and not $\le$