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 $$y ≥ -\frac{2}{3}x - 1$$