Chapter 3: Q270. (page 312)

Graph the linear inequality:
$y \leq \frac{5}{4} x$

Short Answer

Expert verified

The solution is

Step by step solution

Given data

The inequality is

$y \leq \frac{5}{4} x$

Concept used

First, we draw the boundary line $y = \frac{5}{4} x$ .

It is in slope–intercept form $y = m x + b$ .

Where $m = \frac{5}{4}$ and $b = 0$

Here the inequality is $\leq$ .

So, we draw a solid line as below,

Point test

We can see that the point $(1, 0)$ is not on the boundary line.

To check $(1, 0)$ is solution of the inequality or not:

$y \leq \frac{5}{4} x$

$0 \leq \frac{5}{4} \cdot 1$

$0 \leq \frac{5}{4}$

So, $(1, 0)$ is a solution of the inequality $y \leq \frac{5}{4} x$ .

Conclusion

Thus, we shade in the side of the boundary line that includes the point $(1, 0)$ .

The graph will be

All points in the shaded region and on the boundary line represent the solutions to $y \leq \frac{5}{4} x$ .

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Graph the linear inequality:
$y \leq \frac{5}{4} x$

Short Answer

Step by step solution

Given data

Concept used

Point test

Conclusion

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Graph the linear inequality:
$y \leq \frac{5}{4} x$