Chapter 7.1, Problem 65HP

a.

To determine

To write: The related expression and record the power of $x$ .

Answer to Problem 65HP

The correct table is:

Equation	Related Expression	Power of $x$
$y=x$	$x$	$1$
$y=x^2$	$x^2$	$2$
$y=x^3$	$x^3$	$3$

Explanation of Solution

Given information: The given table is:

Equation	Related Expression	Power of $x$	Linear or non linear
$y=x$
$y=x^2$
$y=x^3$

Calculation: : The given table is:

Equation	Related Expression	Power of $x$	Linear or non linear
$y=x$
$y=x^2$
$y=x^3$

The related expression for each equation is the expression on the right side of the equal sign. The power of $x$ is the related expression’s exponent.

Equation	Related Expression	Power of $x$
$y=x$	$x$	$1$
$y=x^2$	$x^2$	$2$
$y=x^3$	$x^3$	$3$

b.

To determine

To draw: The graph of each equation using graphing calculator.

Answer to Problem 65HP

The graph of $y=x$ is:

  

The graph of $y=x^2$ is:

  

The graph of $y=x^3$ is:

  

Explanation of Solution

Given information: The given table is:

Equation	Related Expression	Power of $x$	Linear or non linear
$y=x$
$y=x^2$
$y=x^3$

Calculation: The given table is:

Equation	Related Expression	Power of $x$	Linear or non linear
$y=x$
$y=x^2$
$y=x^3$

The graph of $y=x$ is:

  

The graph of $y=x^2$ is:

  

The graph of $y=x^3$ is:

  

c.

To determine

To classify: The each graph is linear or non linear.

Answer to Problem 65HP

Equation	Related Expression	Power of $x$	Linear or Non Linear
$y=x$	$x$	$1$	Linear
$y=x^2$	$x^2$	$2$	Non Linear
$y=x^3$	$x^3$	$3$	Non Linear

Explanation of Solution

Given information: The given table is:

Equation	Related Expression	Power of $x$	Linear or non linear
$y=x$
$y=x^2$
$y=x^3$

Calculation: : The graph is linear if it is a straight line. From the graphs in part b only $y=x$ was a straight line. The remaining graphs are non collinear.

Equation	Related Expression	Power of $x$	Linear or Non Linear
$y=x$	$x$	$1$	Linear
$y=x^2$	$x^2$	$2$	Non Linear
$y=x^3$	$x^3$	$3$	Non Linear

d.

To determine

To explain: How to find whether an equation , or its related expression is linear or non linear.

Answer to Problem 65HP

The equation $y=x$ is linear and remaining equations are non linear.

Explanation of Solution

Given information: The given table is:

Equation	Related Expression	Power of $x$	Linear or non linear
$y=x$
$y=x^2$
$y=x^3$

Calculation: : If the degree of the equation is one then the equation is linear, Otherwise it is non linear.

Thus, the equation $y=x$ is linear and remaining equations are non linear.