IXL - Graph solutions to two-variable absolute value inequalities (Algebra 2 practice)

Graph this inequality:

≥

First, select the vertex and select another point to graph two rays. You can select the rays to switch between solid and dotted, and select a region to change its shading.

Coordinate plane graph with 4 quadrants, x-axis coordinates from -10 to 10, y-axis coordinates from -10 to 10.

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question

Graph this inequality:

First, select the vertex and select another point to graph two rays. You can select the rays to switch between solid and dotted, and select a region to change its shading.

key idea

The graph of the function

–

is shaped like a V. The vertex is at the point

(

)

The slope to the right of the vertex is

The slope to the left of the vertex is

–

The graph of

–

is the region above the V. The points on the V are not included, so the V should be dotted.

solution

Find

and

–

The graph of the function

–

has a vertex at

(

)

with a slope of 1 to the right of the vertex and a slope of

–

to the left of the vertex.

Plot the vertex at

(

)

Then use the slope to plot another point. Since the slope to the right of the vertex is 1, you can move up 1 and right 1 to plot a point at

(

)

Similarly, since the slope to the left is

–

you can move up 1 and left 1 to plot a point at

(

–

)

The inequality uses the symbol >, so be sure to draw dotted rays. Finally, shade the region above the rays because the inequality starts with

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Teacher tools

Work it out

Not feeling ready yet? These can help:

H.3Graph an absolute value function

F.2Graph a two-variable linear inequality

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