Question

1. which ordered pair is in the solution set of ( y < \frac{3}{5}x - 4 )?

options:

• ( (5, -4) )
• ( (0, 1) )
• ( (-2, -5) )
• ( (-8, 3) )

clear all

Explanation:

Step1: Define the inequality

The given inequality is $y \leq \frac{3}{5}x - 4$. We will test each ordered pair $(x,y)$ by substituting $x$ into the right-hand side and checking if $y$ is less than or equal to the result.

Step2: Test pair (5, -4)

Substitute $x=5$:
$\frac{3}{5}(5) - 4 = 3 - 4 = -1$
Check if $-4 \leq -1$: This is true, but we will verify all pairs to confirm.

Step3: Test pair (9, 1)

Substitute $x=9$:
$\frac{3}{5}(9) - 4 = \frac{27}{5} - 4 = 5.4 - 4 = 1.4$
Check if $1 \leq 1.4$: This is true, but continue testing.

Step4: Test pair (-2, -5)

Substitute $x=-2$:
$\frac{3}{5}(-2) - 4 = -\frac{6}{5} - 4 = -1.2 - 4 = -5.2$
Check if $-5 \leq -5.2$: This is false.

Step5: Test pair (-8, 3)

Substitute $x=-8$:
$\frac{3}{5}(-8) - 4 = -\frac{24}{5} - 4 = -4.8 - 4 = -8.8$
Check if $3 \leq -8.8$: This is false.

Step6: Recheck valid pairs for accuracy

For (5, -4): $-4 \leq -1$ holds. For (9, 1): $1 \leq 1.4$ holds. We confirm both satisfy the inequality, but we ensure we follow the test correctly.

Answer:

(5, -4), (9, 1)