Question

The boundary line on the graph represents the equation 5x + 2y = 6. Write aninequality that is represented by the graph.

Answer 1

You know that this equation represents the boundary line:

`5x+2y=6`

You can solve for "y" in order to write the equation in Slope-Intercept Form:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

Then:

`\begin{gathered} 2y=-5x+6 \\ \\ y=(-5x)/(2)+(6)/(2) \\ \\ y=-(5)/(2)x+3 \end{gathered}`

By definition, when the line is dashed the inequality symbol could be:

`<\text{ or }>`

To determine the symbol, you can observe the graph. Notice that the shaded region is below the line. Then, you can determine that the inequality represented by the graph is:

`y<-(5)/(2)x+3`

Hence, the answer is:

`y<-(5)/(2)x+3`