Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

True or False: The point $\left(-2,-6\right)$ is on the graph of the equation $x=2y-2$. 

Step-by-Step Solution

Answer

The statement is false.

Step 1. Given information

Need to check whether the statement "The point $\left(-2,-6\right)$is on the graph of the equation $x=2y-2$." is true or false.

Step 2. Check

For the point$\left(-2,-6\right)$, need to check whether $x=-2$ and $y=-6$ satisfies the equation $x=2y-2$or not.

$\begin{array}{rcl}x& =& 2y-2\\ -2& =& 2\left(-6\right)-2\\ -2& =& -12-2\\ -2& =& -14\end{array}$

But $-2\ne -14$.

Therefore, the equation is not satisfied.

Step 3. Final answer

The equation is not satisfied, so the point $\left(-2,-6\right)$ is not on the graph.

Therefore, the given statement "The point $\left(-2,-6\right)$ is on the graph of the equation $x=2y-2$" is false.