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Chapter 2: Q18. (page 98)

Graph each inequality.

18..y鈭�2<3x

Short Answer

Expert verified

The graph of the inequality is shown below:

Step by step solution

01

– Find the boundary line equation of the given equation.

Consider the inequality y-2<3x

The boundary line equaton is y-2=3x

Here the inequality is <, graph the boundary line as a dashed line.

Find the slope intercept form of y-2=3x

y鈭�2=3xy=3x+2鈥夆赌夆赌夆赌夆赌塧诲诲2辞苍产辞迟丑蝉颈诲别蝉

The equation y=3x+2is in slope intercept form with slope 3

02

– Choose a test point and test the inequality.

Choose the test point as 0,0.

Substitute x=0,y=0in y-2<3x

y鈭�2<3x0鈭�2<3(0)鈥夆赌夆赌夆赌夆赌夆赌夆赌塻耻产蝉迟颈迟耻迟别0蹿辞谤x,0fory鈭�2<0鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌塼谤耻别

03

– Conclusion

Since, -2<0results a true inequality, so, shade the region that contains the point 0,0.

Graphical representation of y-2<3x

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