Question

“graph the linear inequality 5x+2y <=10 use the graphing tool to graph the inequality”

Answer 1

Step 1. The inequality we have is:

`5x+2y\leq10`

In order to graph this inequality, we will need to solve for y.

-To solve for y, subtract 5x to both sides:

`2y\leq-5x+10`

-Then, divide both sides by 2:

`\begin{gathered} y\leq-(5)/(2)x+(10)/(2) \\ \downarrow \\ y\leq-(5)/(2)x+5 \end{gathered}`

Step 2. The inequality now is:

`y\leq-(5)/(2)x+5`

To graph the inequality, we have to also graph the line:

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

Comparing this line with the slope-intercept equation:

`y=mx+b`

where m is the slope and b is the y-intercept, in our case,

`\begin{gathered} m=-(5)/(2) \\ b=5 \end{gathered}`

Step 3. Graph the line:

Graphing only the line:

here we have also two points where the line passes. This is considering the slope of -5/2 and the y-intercept of 5.

Step 4. Going back to our inequality:

`y\leq-(5)/(2)x+5`

The symbol

≤

indicates that we must also include the values below this line, as shown in the following diagram which represents the graph of the inequality:

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Answer: