Question

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Answer 1

Inequalities are used to represent unequal expressions.

• The inequality is: $y > 2x +1$.
• 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

$(x_1,y_1) = (2,5)$

$(x_2,y_2) = (6,13)$

Calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{13-5}{6-2}$

$m = \frac{8}{4}$

$m =2$

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:

$y > m(x - x_1) + y_2$

This gives

$y > 2(x - 2) + 5$

$y > 2x - 4 + 5$

$y > 2x +1$

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.

$y > 2x +1$

$y > 2\times 10 + 1$

$y > 21$

Read more about inequalities at:

brainly.com/question/20383671