Step 1. The inequality we have is:
[tex]5x+2y\leq10[/tex]
In order to graph this inequality, we will need to solve for y.
-To solve for y, subtract 5x to both sides:
[tex]2y\leq-5x+10[/tex]
-Then, divide both sides by 2:
[tex]\begin{gathered} y\leq-\frac{5}{2}x+\frac{10}{2} \\ \downarrow \\ y\leq-\frac{5}{2}x+5 \end{gathered}[/tex]
Step 2. The inequality now is:
[tex]y\leq-\frac{5}{2}x+5[/tex]
To graph the inequality, we have to also graph the line:
[tex]y=-\frac{5}{2}x+5[/tex]
Comparing this line with the slope-intercept equation:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept, in our case,
[tex]\begin{gathered} m=-\frac{5}{2} \\ b=5 \end{gathered}[/tex]
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:
[tex]y\leq-\frac{5}{2}x+5[/tex]
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:
