Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q22.

Expert-verified

Algebra 2

Found in: Page 66

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.
$y = \sqrt{2 x - 5}$

No, the equation $y = \sqrt{2 x - 5}$ is not a linear equation.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 – Definition of a linear equation and linear function.

In a linear equation the exponent of each variable is 1 and the variables may not be multiplied together. The graph of a linear equation is always a line.

In a linear function, each input value has a unique output value. In other words, for each point in domain, there is a unique value in the range of function. It can be written as $f (x) = m x + b$ , where m and b are real numbers.

Step 2 – Given information.

The given equation is:

$y = \sqrt{2 x - 5}$

Taking square on both sides.

$\begin{array}{l} y^{2} = {(\sqrt{2 x - 5})}^{2} \\ y^{2} = 2 x - 5 \end{array}$

Step 3 – Check whether the equation is linear or not.

In the equation $y^{2} = 2 x - 5$ the exponent of x is 1 and the exponent of y is 2.

The equation $y^{2} = 2 x - 5$ is not a linear equation because y has an exponent other than 1.

The equation $y^{2} = 2 x - 5$ is equivalent to $y = \sqrt{2 x - 5}$ . So, the equation $y = \sqrt{2 x - 5}$ is not linear.

Thus, the required answer is “No” because the equation $y = \sqrt{2 x - 5}$ is not a linear equation.

Most popular questions for Math Textbooks

Find the reciprocal of each number.

$- \frac{2}{3}$

Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function.

$\{(- 5, 2), (2, 4), (1, 1), (- 5, - 2)\}$

Find each value if $f (x) = 5 x - 9$

$f (- 2 v)$

Find the x-intercept and the y-intercept of the graph of each equation. Then graph of the equation.

$2 x + 5 y - 10 = 0$

How many of the first one hundred positive integers contain the digit 7?

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free