Chapter 2: Q22. (page 98)

Graph each inequality.
$x - 6 y + 3 > 0$ .

Short Answer

Expert verified

The graph of the inequality is shown below:

Step by step solution

– Find the boundary line equation of the given equation.

Consider the inequality $x - 6 y + 3 > 0$ .

The boundary line equaton is $x - 6 y + 3 = 0$ .

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

Find the slope intercept form of $x - 6 y + 3 = 0$ :

$\begin{array}{l} x - 6 y + 3 = 0 \\ x - 6 y = - 3 Subtract3frombothsides \\ - 6 y = - x - 3 Subtract x frombothsides \\ y = \frac{- x - 3}{- 6} Dividebothsidesby - 6 \\ y = \frac{1}{6} x + \frac{1}{2} \end{array}$

The slope intercept form is $y = \frac{1}{6} x + \frac{1}{2}$ with slope $\frac{1}{6} .$

– Choose a test point and test the inequality.

Choose the test point as $(0, 0) .$

Substitute $x = 0, y = 0$ in $x - 6 y + 3 > 0$ :

$\begin{array}{l} x - 6 y + 3 > 0 \\ 0 - 6 (0) + 3 > 0 substitute0for x, 0 for y \\ 3 > 0 true \end{array}$

– Conclusion

Since, $3 > 0$ results a true inequality, so, shade the region that contains the point $(0, 0) .$

Graphical representation of $x - 6 y + 3 > 0$ :

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Graph each inequality.
$x - 6 y + 3 > 0$ .

Short Answer

Step by step solution

– Find the boundary line equation of the given equation.

– Choose a test point and test the inequality.

– Conclusion

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Graph each inequality.x-6y+3>0.

Short Answer

Step by step solution

– Find the boundary line equation of the given equation.

– Choose a test point and test the inequality.

– Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Applied Mathematics

Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Graph each inequality.
$x - 6 y + 3 > 0$ .