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McGraw Hill Integrated I, 2012
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McGraw Hill Integrated I, 2012 View details
6. Graphing Inequalities in Two Variables
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Exercise 1 Page 320

To graph the inequality, you have to draw the boundary line, then decide which side of the boundary line to shade.

Practice makes perfect

Graphing an inequality involves two main steps.

  1. Plotting the boundary line.
  2. Shading half of the plane to show the solution set.

Boundary Line

To graph the inequality, we have to draw the boundary line. The equation of a boundary line is written by replacing the inequality symbol from the inequality with an equals sign.

Inequality & Boundary Line y > x+3 & y = x+3 Fortunately, this equation is already in slope-intercept form, so we can identify the slope m and y-intercept (0, b). y= 1x+ 3 We will plot the y-intercept (0, 3), then use the slope m= 1 to plot another point on the line. Connecting these points with a dashed line will give us the boundary line of our inequality. Note that the boundary line is dashed, not solid, because the inequality is strict.

Shading the Plane

To decide which side of the boundary line to shade, we will substitute a test point that is not on the boundary line into the given inequality. If the substitution creates a true statement, we shade the region that includes the test point. Otherwise, we shade the opposite region. Let's use (0,0) as our test point.
y>x+3
SubstituteII

x= 0, y= 0

0 ? > 0 +3
AddTerms

Add terms

0 ≯ 3
Since the substitution of the test point did not create a true statement, we should shade the region that does not contain the test point.
Subchapter links expand_more
arrow_right Check Your Understanding p.320
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arrow_right Practice and Problem Solving p.320-321
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arrow_right H.O.T. Problems p.321
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arrow_right Standardized Test Practice p.322
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arrow_right Spiral Review p.322
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arrow_right Skills Review p.322
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