To determine which ordered pairs satisfy the inequality [tex]\( y < 3x - 7 \)[/tex], we need to test each pair individually. Let's go through each ordered pair step by step:
1. Ordered Pair (0, -7):
[tex]\[
y = -7 \quad \text{and} \quad x = 0
\][/tex]
Substitute [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the inequality:
[tex]\[
-7 < 3(0) - 7
\][/tex]
Simplify the right-hand side:
[tex]\[
-7 < -7
\][/tex]
This inequality is not true because [tex]\(-7\)[/tex] is not less than [tex]\(-7\)[/tex], hence [tex]\((0, -7)\)[/tex] is not a solution.
2. Ordered Pair (4, 2):
[tex]\[
y = 2 \quad \text{and} \quad x = 4
\][/tex]
Substitute [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the inequality:
[tex]\[
2 < 3(4) - 7
\][/tex]
Simplify the right-hand side:
[tex]\[
2 < 12 - 7
\][/tex]
[tex]\[
2 < 5
\][/tex]
This inequality is true because [tex]\(2\)[/tex] is less than [tex]\(5\)[/tex], hence [tex]\((4, 2)\)[/tex] is a solution.
3. Ordered Pair (0, 0):
[tex]\[
y = 0 \quad \text{and} \quad x = 0
\][/tex]
Substitute [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the inequality:
[tex]\[
0 < 3(0) - 7
\][/tex]
Simplify the right-hand side:
[tex]\[
0 < -7
\][/tex]
This inequality is not true because [tex]\(0\)[/tex] is not less than [tex]\(-7\)[/tex], hence [tex]\((0, 0)\)[/tex] is not a solution.
4. Ordered Pair (-3, 2):
[tex]\[
y = 2 \quad \text{and} \quad x = -3
\][/tex]
Substitute [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the inequality:
[tex]\[
2 < 3(-3) - 7
\][/tex]
Simplify the right-hand side:
[tex]\[
2 < -9 - 7
\][/tex]
[tex]\[
2 < -16
\][/tex]
This inequality is not true because [tex]\(2\)[/tex] is not less than [tex]\(-16\)[/tex], hence [tex]\((-3, 2)\)[/tex] is not a solution.
After evaluating all the ordered pairs, the one that satisfies the inequality [tex]\( y < 3x - 7 \)[/tex] is:
[tex]\[
(4, 2)
\][/tex]
