Question

algebra 1
graphing inequalities: s
sketch the graph of each linear inequality

1. $9x - 5y \leq 25$

Explanation:

Step1: Rearrange to slope-intercept form

Start with the given inequality and solve for $y$:
$$9x - 5y \leq 25$$
$$-5y \leq -9x + 25$$
Divide by $-5$ (reverse inequality sign):
$$y \geq \frac{9}{5}x - 5$$

Step2: Identify boundary line

The boundary line is the equation $y = \frac{9}{5}x - 5$.

• Y-intercept: $(0, -5)$
• Slope: $\frac{9}{5}$ (rise 9, run 5)

Since the inequality is $\geq$, the line is solid.

Step3: Determine shaded region

Test the origin $(0,0)$ in the original inequality:
$$9(0) - 5(0) \leq 25 \implies 0 \leq 25$$
This is true, so shade the region above the boundary line (including the line itself).

Answer:

1. Draw a solid line with y-intercept $(0, -5)$ and slope $\frac{9}{5}$ (plot a second point by moving 5 right and 9 up from $(0,-5)$ to get $(5,4)$).
2. Shade the entire region above and including this solid line.