point in the solution set. \[ y<-\frac{2}{3} x+5 \]

To find a point in the solution set of the inequality \[ y < -\frac{2}{3} x + 5, \] we can follow these steps: 1. **Understand the inequality**: The inequality represents all the points below the line defined by the equation \(y = -\frac{2}{3} x + 5\). 2. **Find the line's intercepts**: - **Y-intercept**: Set \(x = 0\): \[ y = -\frac{2}{3}(0) + 5 = 5. \] So, the y-intercept is \((0, 5)\). - **X-intercept**: Set \(y = 0\): \[ 0 = -\frac{2}{3} x + 5 \implies \frac{2}{3} x = 5 \implies x = \frac{5 \cdot 3}{2} = \frac{15}{2} = 7.5. \] So, the x-intercept is \((7.5, 0)\). 3. **Choose a point below the line**: We can select a point that is clearly below the line. For example, let's choose \(x = 0\): - Substitute \(x = 0\) into the inequality: \[ y < -\frac{2}{3}(0) + 5 \implies y < 5. \] - A point that satisfies this condition is \( (0, 4) \) since \(4 < 5\). Thus, a point in the solution set of the inequality \(y < -\frac{2}{3} x + 5\) is \[ (0, 4). \]