graph the inequality on the axes below.\n$-3x + 4y < 4$

Explanation:

Step1: Rewrite in slope-intercept form

Rearrange to solve for $y$: $$-3x + 4y < 4$$ $$4y < 3x + 4$$ $$y < \frac{3}{4}x + 1$$

Step2: Identify boundary line

The boundary is $y = \frac{3}{4}x + 1$. Since the inequality is $<$, use a dashed line.

• y-intercept: $(0, 1)$
• Slope: $\frac{3}{4}$ (rise 3, run 4)

Step3: Test a point for shading

Use $(0,0)$: $$0 < \frac{3}{4}(0) + 1$$ $$0 < 1$$ This is true, so shade the region containing $(0,0)$.

Answer:

1. Draw a dashed line through points $(0, 1)$ and $(4, 4)$ (from slope $\frac{3}{4}$).
2. Shade the region below this dashed line (the area that includes the origin $(0,0)$).