Question

this is the graph of a linear inequality. write the inequality in slope-intercept form.
write your answer with y first, followed by an inequality symbol. use integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify line intercepts

The dashed line crosses the y-axis at $(0,6)$ and the x-axis at $(8,4)$ (wait, correction: using points $(-8,8)$ and $(8,4)$ to calculate slope)

Step2: Calculate slope of the line

Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 8}{8 - (-8)} = \frac{-4}{16} = -\frac{1}{4}$

Step3: Write line equation (slope-intercept)

Using y-intercept $(0,6)$, the line is $y = -\frac{1}{4}x + 6$

Step4: Determine inequality symbol

The shaded region is below the dashed line, so use $\leq$ (wait, no: dashed line means strict inequality? Wait no, shaded area includes points below the line, and dashed line means the line itself is not included. Wait, check the shaded area: at $x=0$, shaded area is below $y=6$, so $y < -\frac{1}{4}x + 6$? Wait no, wait point $(0,0)$ is in shaded area: plug into $y$ vs $-\frac{1}{4}x +6$: $0 < 6$, which is true. And the line is dashed, so the inequality is strict.
Wait correction: confirm points: when $x=-8$, $y=8$; $x=0$, $y=6$; $x=8$, $y=4$. Slope is $\frac{6-8}{0-(-8)} = \frac{-2}{8} = -\frac{1}{4}$, correct. Y-intercept is 6, so line is $y = -\frac{1}{4}x +6$. Shaded area is below the dashed line, so inequality is $y < -\frac{1}{4}x +6$? Wait no, wait $(0,6)$ is on the dashed line, not included, and shaded area is all points where y is less than the line's y-value for each x.

Wait another check: take point $(8,4)$ is on the line, shaded area includes $(8,0)$ which is $0 < -\frac{1}{4}(8)+6 = -2 +6=4$, which is true. Correct.

Answer:

$y < -\frac{1}{4}x + 6$