How to graph a two-step inequality

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Algebra › How to graph a two-step inequality

Questions 1 - 1

Which graph depicts the following inequality?

$x\geq4y+12$

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No real solution.

Let's put the inequality in slope-intercept form to make it easier to graph:

$x\geq4y+12$

$x-12\geq4y+12-12$

$x-12\geq4y$

$\frac{x-12}{4}\geq\frac{4y}{y}$

$\frac{1}{4}x-3\geq y$

The inequality is now in slope-intercept form. Graph a line with slope $\frac{1}{4}$ and y-intercept .

Because the inequality sign is greater than or equal to, a solid line should be used.

Next, test a point. The origin is good choice. Determine if the following statement is true:

$\frac{1}{4}(0)-3\geq0$

The statement is false. Therefore, the section of the graph that does not contain the origin should be shaded.