Q. 24 In Problems 21鈥�28, determine w... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 3: Q. 24 (page 136)

In Problems 21鈥�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 $\frac{鈭� y}{鈭� x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

x	y	$\frac{鈭� y}{鈭� x}$
-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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91影视

In Problems 21鈥�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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91影视

In Problems 21鈥�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

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 21鈥�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