Given:
Two points on the line are (0, 4) and (2, 0).
To write: The inequality in slope form for the graph.
Explanation:
Using the two-point formula,
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]
Substituting the points we get,
[tex]\begin{gathered} \frac{y-4}{0-4}=\frac{x-0}{2-0} \\ \frac{y-4}{-4}=\frac{x-0}{2} \\ y-4=-\frac{4x}{2} \\ y-4=-2x \\ y=-2x+4 \end{gathered}[/tex]
Since the shaded region is above the line.
So, the inequality becomes,
[tex]y\ge-2x+4[/tex]
Final answer: The inequality in slope form for the graph is,
[tex]y\ge-2x+4[/tex]
