Question

Write an inequality in slope form for the graph below.

Answer 1

Given:

Two points on the line are (0, 4) and (2, 0).

To write: The inequality in slope form for the graph.

Step-by-step explanation:

Using the two-point formula,

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

Substituting the points we get,

`\begin{gathered} (y-4)/(0-4)=(x-0)/(2-0) \\ (y-4)/(-4)=(x-0)/(2) \\ y-4=-(4x)/(2) \\ y-4=-2x \\ y=-2x+4 \end{gathered}`

Since the shaded region is above the line.

So, the inequality becomes,

`y\ge-2x+4`

Final answer: The inequality in slope form for the graph is,

`y\ge-2x+4`