Question

graph the following linear inequalities on the coordinate plane provided.

1. ( y leq \frac{4}{3}x - 4 )
2. ( y > 2x - 6 )
3. ( y > -3x + 4 )
4. ( y geq -\frac{3}{2}x + 3 )
5. ( y < x - 5 )
6. ( y geq -\frac{1}{2}x - 3 )

Explanation:

9. \(y \leq \frac{4}{3}x - 4\)

1. Draw solid line \(y = \frac{4}{3}x - 4\) (slope \(\frac{4}{3}\), y-intercept -4).
2. Shade below the line.

10. \(y > 2x - 6\)

1. Draw dashed line \(y = 2x - 6\) (slope 2, y-intercept -6).
2. Shade above the line.

11. \(y > -3x + 4\)

1. Draw dashed line \(y = -3x + 4\) (slope -3, y-intercept 4).
2. Shade above the line.

12. \(y \geq -\frac{3}{2}x + 3\)

1. Draw solid line \(y = -\frac{3}{2}x + 3\) (slope \(-\frac{3}{2}\), y-intercept 3).
2. Shade above the line.

13. \(y < x - 5\)

1. Draw dashed line \(y = x - 5\) (slope 1, y-intercept -5).
2. Shade below the line.

14. \(y \geq -\frac{1}{2}x - 3\)

1. Draw solid line \(y = -\frac{1}{2}x - 3\) (slope \(-\frac{1}{2}\), y-intercept -3).
2. Shade above the line.

(Note: To graph, plot two points per line (e.g., for 9: (0,-4) and (3,0)), draw the line with correct style (solid/dashed), then test a point (like (0,0)) to confirm shading direction.)

Answer:

(Graphing instructions for each inequality are provided below)