### About Linear Inequalities in two Variables:

To graph a linear inequality in two variables we solve our inequality for y and replace the inequality symbol with an equality symbol. We then graph this equality as our boundary line. The boundary line separates the solution region from the non-solution region. We can then shade above the boundary line for a greater than, or below the line for a less than.

Test Objectives

- Demonstrate the ability to place an equation in slope-intercept form
- Demonstrate the ability to graph a boundary line
- Demonstrate the ability to graph a linear inequality in two variables

#1:

Instructions: Graph each linear inequality.

a) $$7x - 3y ≥ -15$$

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#2:

Instructions: Graph each linear inequality.

a) $$y ≥ 7$$

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#3:

Instructions: Graph each linear inequality.

a) $$5x + 3y < 12$$

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#4:

Instructions: Graph each compound inequality.

a) $$6x + y < 3$$ or $$6x + y ≥ 6$$

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#5:

Instructions: Graph each compound inequality.

a) $$x ≤ -3$$ and $$2x + 3y ≥ -3$$

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Written Solutions:

#1:

Solutions:

a) $$y ≤ \frac{7}{3}x + 5$$

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#2:

Solutions:

a) $$y ≥ 7$$

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#3:

Solutions:

a) $$y < -\frac{5}{3}x + 4$$

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#4:

Solutions:

a) $$y < -6x + 3$$ or $$y≥ -6x + 6$$

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#5:

Solutions:

a) $$x ≤ -3$$ and $$y ≥ -\frac{2}{3}x - 1$$