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: Find slope of the line

The line passes through $(0,1)$ and $(2,0)$.
Slope $m = \frac{0-1}{2-0} = -\frac{1}{2}$

Step2: Identify y-intercept

The line crosses the y-axis at $(0,1)$, so $b=1$.
Slope-intercept form of the line: $y = -\frac{1}{2}x + 1$

Step3: Determine inequality symbol

The line is dashed, and the shaded region is below the line. Use $\leq$? No, dashed means strict? Wait no, shaded below dashed line: $y < -\frac{1}{2}x + 1$? Wait no, check point (0,0): $0 < -\frac{1}{2}(0)+1$ → $0<1$, which is true, and (0,0) is shaded. Correct.

Answer:

$y \leq -\frac{1}{2}x + 1$? Wait no, dashed line means no equality. Wait the line is dashed, so it's $y < -\frac{1}{2}x + 1$. Wait let's confirm: the line goes through (0,1) and (2,0). Shaded area is below the dashed line, so the inequality is $y < -\frac{1}{2}x + 1$.

Wait correction:

Step3: Check line type and shading

Dashed line → no equality. Shading below line → use $<$.
Final inequality: $y < -\frac{1}{2}x + 1$