Question

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2), and (1, negative 1). Everything to the right of the line is shaded.
The solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution?

(0, 2)
(2, 0)
(1, −2)
(−2, 1)

Answer 1

To determine which point is a solution to the inequality \( y > -3x + 2 \), we can evaluate each point to see if they satisfy the inequality.

1. **Point (0, 2)**:
\[
y > -3(0) + 2 \Rightarrow 2 > 2 \quad \text{(false)}
\]

2. **Point (2, 0)**:
\[
y > -3(2) + 2 \Rightarrow 0 > -6 + 2 \Rightarrow 0 > -4 \quad \text{(true)}
\]

3. **Point (1, -2)**:
\[
y > -3(1) + 2 \Rightarrow -2 > -3 + 2 \Rightarrow -2 > -1 \quad \text{(false)}
\]

4. **Point (-2, 1)**:
\[
y > -3(-2) + 2 \Rightarrow 1 > 6 + 2 \Rightarrow 1 > 8 \quad \text{(false)}
\]

From the evaluations, the only point that satisfies the inequality \( y > -3x + 2 \) is:

**(2, 0)**.