Chapter 3: Q. 24 (page 136)

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .
x $y = f (x)$
-2 -4
-1 0
0 4
1 8
2 12

Short Answer

Expert verified

The function is linear and the equation of the line is $f (x) = 4 x + 4$

Step by step solution

Step 1. Given Information

x	$y = f (x)$
-2	-4
-1	0
0	4
1	8
2	12

The data in the table represent values of y with respect to x.

Compute the average rate of change of each function.

If the average rate of change is constant, then the function is linear.
If the average rate of change is not constant, then the function is nonlinear.

Step 2. Calculation

Calculate average rate of change by the formula $\frac{∆ y}{∆ x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

x	y	$\frac{∆ y}{∆ x}$
-2	-4	4
-1	0	4
0	4	4
1	8	4
2	12

The average rate of change is constant, so the function is linear.

Step 3. Find equation of line.

The average rate of change is $m = 4$ and a point from given data $(- 2, - 4)$ .

Use slope point form to find equation of the line.

$y - y_{1} = m (x - x_{1}) y - (- 4) = 4 (x - (- 2)) y + 4 = 4 x + 8 y = 4 x + 4$

Step 4. Conclusion

As average rate of change is constant, so function is linear and the equation of the line is $f (x) = 4 x + 4$

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In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .
x $y = f (x)$
-2 -4
-1 0
0 4
1 8
2 12

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Find equation of line.

Step 4. Conclusion

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In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .xy=f(x)-2-4-100418212

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Find equation of line.

Step 4. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Probability and Statistics

Pure Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .
x $y = f (x)$
-2 -4
-1 0
0 4
1 8
2 12