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Level 1 - Writing and Graphing Equations in Slope-Intercept Form - Writing and Graphing Linear Relationships (Algebra 1)

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Writing and Graphing Equations in Point-Slope Form - Writing and Graphing Linear Relationships (Algebra 1)

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This lesson will be finished by finding the solution set of two linear inequalities. Consider the following inequalities. y > x - 3 y ≤ 4x + 1 To graph the solution set of these two inequalities, it is important to identify and graph both boundary lines. Note that the inequalities are already written in slope-intercept form. The slope and the y-intercept can be used to graph these lines. Also, the boundary line of the strict inequality is dashed, while the boundary line of the non-strict inequality is solid.

Next, the the point ( 0, 0) is substituted in each inequality to see if these are satisfied.

Inequality

Substitute

Simplify

y > x - 3

0 ? > 0 - 3

0 > -3 ✓

y ≤ 4x + 1

0 ? ≤ 4( 0) + 1

0 ≤ 1 ✓

The coordinates of the point satisfy both inequalities.

Since (0,0) is above the line y=x-3, the entire region above this line should be shaded.

Since (0,0) is below the line y=4x+1, the entire region below this line should be shaded.

This information can be shown in the graph.

Finally, the overlapping region is the solution set for both inequalities. This means that the points in this region satisfy both inequalities at the same time.

A single inequality divides the coordinate plane in two regions, and one of those regions is the solution set of the inequality. Meanwhile, two inequalities can divide the coordinate plane in up to four regions, and sometimes there is no overlapping solutions for both inequalities at the same time.

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This lesson will be finished by finding the solution set of two linear inequalities. Consider the following inequalities. y > x - 3 y ≤ 4x + 1 To graph the solution set of these two inequalities, it is important to identify and graph both boundary lines.

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Did you know: Our worksheets can be printed, downloaded and used on computer or mobile in the eCourses subchapters

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Wordwall - Create better lessons quicker

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Maze chase - Run to the correct answer zone, whilst avoiding the enemies.

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Wordwall - Create better lessons quicker

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Linear Functions and Inequalities Review

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Flash cards - Test yourself using cards with prompts on the front and answers on the back.