deltamath\n← back to home\nlinear inequality systems graphically\ndue: march 4 at 6:00 pm\ngrade…

deltamath\n← back to home\nlinear inequality systems graphically\ndue: march 4 at 6:00 pm\ngrade: 63%\nlinear inequality systems graphically\ngraphing linear inequalities\n✓ solve linear system graphically (lev. 1)\nmatch graph/equation ax + by = c (mc)\ngraphing ax + by = c from intercepts\nscientific calculator\ngraphing calculator\nemanuelly mara dos santos pereira log out\ngraph the inequality on the axes below.\n$-3x + 4y \\leq -4$

Answer

Explanation:

Step1: Rewrite in slope-intercept form

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

Step2: Identify boundary line

The boundary line is $y = \frac{3}{4}x - 1$. Since the inequality is $\leq$, the line is solid.

x-intercept: Set $y=0$, $0 = \frac{3}{4}x - 1 \implies x = \frac{4}{3} \approx 1.33$
y-intercept: Set $x=0$, $y = -1$

Step3: Determine shaded region

Test the origin $(0,0)$ in the original inequality: $$-3(0) + 4(0) \leq -4 \implies 0 \leq -4$$ This is false, so shade the region not containing the origin (below the boundary line).

Answer:

Draw a solid line through points $\left(\frac{4}{3}, 0\right)$ and $(0, -1)$ (with slope $\frac{3}{4}$).
Shade the area below this solid line.