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

this is the graph of a linear inequality. write the inequality in slope-intercept form.\n\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.\n\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

The line crosses the y-axis at $(0, 4)$, so $b = 4$.

Step2: Calculate the slope

Using points $(0, 4)$ and $(-1, 0)$, the slope $m$ is: $$m = \frac{0 - 4}{-1 - 0} = \frac{-4}{-1} = 4$$

Step3: Determine the inequality symbol

The line is solid, and the shaded region is to the left/above the line. Testing $(0, 0)$: $0 \leq 4(0) + 4$ is true, but the origin is not shaded. Testing $(-2, 0)$: $0 \geq 4(-2) + 4 \Rightarrow 0 \geq -4$ is true, and $(-2, 0)$ is shaded.

Step4: Write the final inequality

Combine the slope, intercept, and symbol into slope-intercept form $y \geq mx + b$. $$y \geq 4x + 4$$

Answer:

y \geq 4x + 4