Chapter 1.2, Problem 87E

To determine

To find: if the given statement is true or false.

Answer to Problem 87E

False

Explanation of Solution

Given:

The statement, “The graph of a linear equation cannot be symmetric with respect to the origin.”

Concept used:

The graph of an equation is symmetric with respect to the origin when replacing $\left(x,y\right)$ with $\left(-x,-y\right)$ yields an equivalent equation.

Given statement is not true since there exists linear equations which are symmetric with respect to origin.

For example, consider the linear equation $y=x$ .

Now replace $x$ with $-x$ and $y$ with $-y$ ,

  $\begin{array}{c}-y=-x\\ y=x\end{array}$

It results in equivalent equation.

Thus $y=x$ is symmetric with respect to origin.

Conclusion:

The given statement is wrong