Question

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

Answer 1

Step 1. The expression we have for the graph is:

`6=5x+2y`

To find the inequality that represents the graph, we need to solve for y first.

Step 2. Solve for y in the equation:

`6=5x+2y`

We can also represent this as follows:

`5x+2y=6`

Move 5x to the right side as a -5x:

`2y=-5x+6`

Move the two that is multiplying on the left side, to divide on the right side:

`y=(-5x+6)/(2)`

Simplify:

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

This is the equation of the line.

Step 3. Find the inequality.

Since the shaded part is below the line, and it has a dotted line, the inequality that represents this is:

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

Which are the values below the dotted line.

Answer:

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