Question

Determine the inequality shown in the graph below. The inequalitysymbols can be entered using the toolbar.See picture

Answer 1

Let's first identify at least two points that pass through the graph,

GENERATING THE EQUATION:

Points: 0, 3 and 8,5

a.) The slope of the line

`\text{ Slope = }(y_2-y_1)/(x_2-x_1)\text{ = }\frac{\text{ 5 - 3}}{\text{ 8 - 0}}\text{ = }(2)/(8)\text{ = }(1)/(4)`

b.) The y-intercept. Use x, y = 0, 3 and m = 1/4

`\text{ y = mx + b}`
`\text{ 3 = }(1)/(4)(0)\text{ + b}`
`\text{ b = 3}`

c.) Complete the equation. Plug-in m = 1/4 and b = 3 in y = mx + b.

`\text{ y = mx + b}`
`\text{ y = }(1)/(4)\text{x + 3}`

NOTES:

≤ or ≥ → Solid line

< or > → Dotted line

> or ≥ → Shading above

≤ or < → Shading below

The graph shown is has a dotted line graph and shaded below.

The formula of the given inequality will be:

`\begin{gathered} \text{ y < }(1)/(4)\text{x + 3} \\ \end{gathered}`