Question

Which point is a solution to y ≤ 4x + 5?

(-4,0)
(0, -2)
(-6,4)
(0,10)

Answer 1

To determine which point is a solution to the inequality \( y \leq 4x + 5 \), we need to check each point by substituting the x and y coordinates into the inequality.

1. For the point \((-4, 0)\):
\[
y = 0, \quad x = -4
\]
\[
0 \leq 4(-4) + 5 \implies 0 \leq -16 + 5 \implies 0 \leq -11 \quad \text{(false)}
\]

2. For the point \((0, -2)\):
\[
y = -2, \quad x = 0
\]
\[
-2 \leq 4(0) + 5 \implies -2 \leq 0 + 5 \implies -2 \leq 5 \quad \text{(true)}
\]

3. For the point \((-6, 4)\):
\[
y = 4, \quad x = -6
\]
\[
4 \leq 4(-6) + 5 \implies 4 \leq -24 + 5 \implies 4 \leq -19 \quad \text{(false)}
\]

4. For the point \((0, 10)\):
\[
y = 10, \quad x = 0
\]
\[
10 \leq 4(0) + 5 \implies 10 \leq 0 + 5 \implies 10 \leq 5 \quad \text{(false)}
\]

The only point that satisfies the inequality \( y \leq 4x + 5 \) is \((0, -2)\).