this is the graph of a linear inequality. write the inequality in slope-intercept form.\nwrite your answer…

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

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

Answer

Explanation:

Step1: Identify the y-intercept of the boundary line

The line crosses the y-axis at $(0, -1)$, so $b = -1$.

Step2: Identify another point and calculate the slope

The line passes through $(-2, 0)$. Using $m = \frac{y_2 - y_1}{x_2 - x_1}$: $$m = \frac{0 - (-1)}{-2 - 0} = \frac{1}{-2} = -\frac{1}{2}$$

Step3: Determine the inequality symbol

The line is dashed, indicating $<$ or $>$. The shaded region is below the line, indicating $<$.

Step4: Write the inequality in slope-intercept form

Substitute $m = -\frac{1}{2}$ and $b = -1$ into $y < mx + b$. $$y < -\frac{1}{2}x - 1$$

Answer:

$y < -\frac{1}{2}x - 1$