Question

1. the graph of (y = -\frac{1}{4}x + 4) is shown on the grid.

choose the ordered pairs that are in the solution set of (y > -\frac{1}{4}x + 4).

((0, 0)) ((-7, 9)) ((0, 8)) ((4, 3)) ((9, 1)) ((5, 5))

Explanation:

Define the inequality

The given inequality is:

$$y > -\frac{1}{4}x + 4$$

Test the ordered pair (0, 0)

Using the Linear Inequalities and Ordered Pairs knowledge points:

$$0 > -\frac{1}{4}(0) + 4 \implies 0 > 4 \quad (\text{False})$$

Test the ordered pair (-7, 9)

Using the Linear Inequalities and Ordered Pairs knowledge points:

$$9 > -\frac{1}{4}(-7) + 4 \implies 9 > 1.75 + 4 \implies 9 > 5.75 \quad (\text{True})$$

Test the ordered pair (0, 8)

Using the Linear Inequalities and Ordered Pairs knowledge points:

$$8 > -\frac{1}{4}(0) + 4 \implies 8 > 4 \quad (\text{True})$$

Test the ordered pairs (4, 3), (9, 1), and (5, 5)

Using the Linear Inequalities and Ordered Pairs knowledge points:
For \((4, 3)\):

$$3 > -\frac{1}{4}(4) + 4 \implies 3 > -1 + 4 \implies 3 > 3 \quad (\text{False})$$

For \((9, 1)\):

$$1 > -\frac{1}{4}(9) + 4 \implies 1 > -2.25 + 4 \implies 1 > 1.75 \quad (\text{False})$$

For \((5, 5)\):

$$5 > -\frac{1}{4}(5) + 4 \implies 5 > -1.25 + 4 \implies 5 > 2.75 \quad (\text{True})$$

Answer:

\((-7, 9)\), \((0, 8)\), and \((5, 5)\)