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Chapter 2: Q14. (page 98)

Graph each inequality.

14.3鈮�x-3y.

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 inequality3鈮�x-3y.

The boundary line equaton is x-3y=3.

Here the inequality is鈮�, graph the boundary line as a solid line.

Find the slope intercept ofx-3y=3:

x鈭�3y=3鈭�3y=3鈭�x鈥夆赌夆赌夆赌夆赌塻耻产迟谤补肠迟xfrombothsidesy=3鈭�x鈭�3鈥夆赌夆赌夆赌夆赌塪颈惫颈诲别产辞迟丑蝉颈诲别蝉产测鈭�3y=x3鈭�1鈥夆赌夆赌夆赌夆赌塻颈尘辫濒颈蹿测

So, the slope intercept form is y=x3-1.

02

– Choose a test point and test the inequality.

Choose the test point as 0,0.

Substitute x=0,y=0in3\gex-3y

3鈮�x鈭�3y3鈮�0鈭�3(0)鈥夆赌夆赌夆赌塻耻产蝉迟颈迟耻迟别0蹿辞谤x,0fory3鈮�0鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌涂谤耻别

03

– Conclusion

Since, 3鈮�0results a true inequality, so, shade the region that contains the point 0,0.

Graphical representation of3\gex-3y

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