Inequalities are used to represent unequal expressions.
- The inequality is: [tex]y > 2x +1[/tex].
- A real world situation is: The number of boys in a class is 1 more than twice the number of girls
The inequality
From the attached graph, we have the following points
[tex](x_1,y_1) = (2,5)[/tex]
[tex](x_2,y_2) = (6,13)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{13-5}{6-2}[/tex]
[tex]m = \frac{8}{4}[/tex]
[tex]m =2[/tex]
On the graph, we have the following observations:
- The line of the graph is a dashed line (this represents > or <)
- The upper part is shaded (this represents >)
So, the inequality is:
[tex]y > m(x - x_1) + y_2[/tex]
This gives
[tex]y > 2(x - 2) + 5[/tex]
[tex]y > 2x - 4 + 5[/tex]
[tex]y > 2x +1[/tex]
Real world situation
A real world situation is:
The number of boys in a class is 1 more than twice the number of girls
The number of boys would be on the y-axis, while the number of girls would be on the x-axis.
A point in the solution set is (10, 21).
i.e.
[tex]y > 2x +1[/tex]
[tex]y > 2\times 10 + 1[/tex]
[tex]y > 21[/tex]
Read more about inequalities at:
https://brainly.com/question/20383671
