Question

Where do you plot points for y ≤ -3/4x + 5

Answer 1

To plot points for the inequality \( y \leq -\frac{3}{4}x + 5 \), follow these steps:

1. **Graph the Boundary Line**: First, graph the boundary line represented by the equation \( y = -\frac{3}{4}x + 5 \). This line can be drawn by finding two points:

- **Y-Intercept**: Set \( x = 0 \):
\[
y = -\frac{3}{4}(0) + 5 = 5
\]
So one point is \( (0, 5) \).

- **X-Intercept**: Set \( y = 0 \) and solve for \( x \):
\[
0 = -\frac{3}{4}x + 5 \implies \frac{3}{4}x = 5 \implies x = \frac{5 \times 4}{3} = \frac{20}{3} \approx 6.67
\]
So another point is \( \left(\frac{20}{3}, 0\right) \).

Plot these two points and draw a solid line through them since the inequality is "less than or equal to," indicating that points on the line are included in the solution.

2. **Shade the Correct Area**: Since the inequality is \( y \leq -\frac{3}{4}x + 5 \), shade the area below the line, which represents all the points where \( y \) is less than or equal to the value given by the line.

3. **Plot Additional Points**: If you want to find more specific points in the shaded region, you can choose values for \( x \) and calculate the corresponding \( y \) values using the equation \( y = -\frac{3}{4}x + 5 \):
- For \( x = 4 \):
\[
y = -\frac{3}{4}(4) + 5 = -3 + 5 = 2 \quad \text{(point (4, 2))}
\]
- For \( x = 8 \):
\[
y = -\frac{3}{4}(8) + 5 = -6 + 5 = -1 \quad \text{(point (8, -1))}
\]

Make sure these points lie below the line when plotted.

By following these steps, you can clearly represent and plot the solution to the inequality \( y \leq -\frac{3}{4}x + 5 \).