Question

Select the correct answer. Choose the system of inequalities that best matches the graph below.

Answer 1

Considering the linear functions on the graph, the inequality that matches the situation is:

B.

• $y \geq \frac{1}{2}x + 2$

• $y \leq 2x + 1$

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The lower bound of the interval is a linear function with y-intercept of b = 2, that also passes through (2,3), hence the slope is:

m = (3 - 2)/(2 - 0) = 1/2.

Hence the inequality is:

$y \geq \frac{1}{2}x + 2$

The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:

m = (5 - 1)/(2 - 0) = 2.

Hence the inequality is:

$y \leq 2x + 1$

More can be learned about linear functions at brainly.com/question/24808124

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