Solving Linear Inequalities in Two Variables
Step 1. Graph the given inequality as if it were an equation using the slope intercept form. If the inequality is > or <, use a dotted line. If the inequality is > or <, use a solid line.
Step 2. Pick a "test point" that is not on the line you graphed in step 1 and plug it into the given inequality. Simplify both sides of the statement.
Step 3. If the test point yields a true statement, shade the side of the line that contains the test point. If the test point yields a false statement, shade the opposite side of the line to the side that contains the test point.
Directions: Please solve the following linear inequality.
2x-3y<9
Step 1. Graph the given inequality as if it were an equation using the slope intercept form. If the inequality is > or <, use a dotted line. If the inequality is > or <, use a solid line.
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2x-3y<9 -3y<-2x+9 y>2/3*x-3 |
Get the statement in y=mx+b form. Flip the symbol, because you divide by a negative. Put a dot on –3 on the y axis then apply a slope of 2/3. Connect the dots with a dotted line. |
Step 2. Pick a "test
point" that is not on the line you graphed in step 1 and
plug it into the given inequality. Simplify both sides of the
statement.
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2(0)-3(0)<9 0–0<9 0<9 TRUE |
Use (0,0) as a test point. |
Step 3. If the test point yields a true statement, shade the side of the line that contains the test point. If the test point yields a false statement, shade the opposite side of the line to the side that contains the test point.
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Because (0,0) yielded a true statement, we need to shade the side of the line that contains (0,0). |
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Directions: Please solve the following linear inequalities.
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