To determine which point satisfies the inequality [tex]\( y \leq 4x + 5 \)[/tex], we need to test each point individually by substituting the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values into the inequality.
Let's evaluate each point:
A. For the point [tex]\((-6, 4)\)[/tex]:
- Substitute [tex]\(x = -6\)[/tex] and [tex]\(y = 4\)[/tex] into the inequality:
[tex]\[ 4 \leq 4(-6) + 5 \][/tex]
[tex]\[ 4 \leq -24 + 5 \][/tex]
[tex]\[ 4 \leq -19 \][/tex]
- This is not true; hence, [tex]\((-6, 4)\)[/tex] does not satisfy the inequality.
B. For the point [tex]\((0, 10)\)[/tex]:
- Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = 10\)[/tex] into the inequality:
[tex]\[ 10 \leq 4(0) + 5 \][/tex]
[tex]\[ 10 \leq 0 + 5 \][/tex]
[tex]\[ 10 \leq 5 \][/tex]
- This is not true; hence, [tex]\((0, 10)\)[/tex] does not satisfy the inequality.
C. For the point [tex]\((0, -2)\)[/tex]:
- Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = -2\)[/tex] into the inequality:
[tex]\[ -2 \leq 4(0) + 5 \][/tex]
[tex]\[ -2 \leq 0 + 5 \][/tex]
[tex]\[ -2 \leq 5 \][/tex]
- This is true; hence, [tex]\((0, -2)\)[/tex] does satisfy the inequality.
D. For the point [tex]\((-4, 0)\)[/tex]:
- Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 0\)[/tex] into the inequality:
[tex]\[ 0 \leq 4(-4) + 5 \][/tex]
[tex]\[ 0 \leq -16 + 5 \][/tex]
[tex]\[ 0 \leq -11 \][/tex]
- This is not true; hence, [tex]\((-4, 0)\)[/tex] does not satisfy the inequality.
Therefore, the point that is a solution to [tex]\( y \leq 4x + 5 \)[/tex] is:
C. [tex]\((0, -2)\)[/tex]
