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Chapter 4: Problem 9

Complete the table of values and graph each equation. $$ x=-\frac{4}{9} $$ $$ \begin{array}{c|c} x & y \\ \hline & 5 \\ \hline & 0 \\ \hline & -1 \\ \hline & -2 \\ \hline \end{array} $$

Short Answer

Expert verified
The completed table is: \[ \begin{array}{c|c} x & y \\ \hline -\frac{4}{9} & 5 \\ \hline -\frac{4}{9} & 0 \\ \hline -\frac{4}{9} & -1 \\ \hline -\frac{4}{9} & -2 \\ \hline \end{array} \] Plot the coordinates and draw a vertical line through the points to represent the equation \(x = -\frac{4}{9}\). The line is parallel to the y-axis.

Step by step solution

01

Find the x-values for the given y-values

Since the equation is x = -\frac{4}{9}, the x-value remains constant for all the y-values. Therefore, the x-value for each of the given y-values is -\frac{4}{9}. Now, the table will look like this: \[ \begin{array}{c|c} x & y \\ \hline -\frac{4}{9} & 5 \\ \hline -\frac{4}{9} & 0 \\ \hline -\frac{4}{9} & -1 \\ \hline -\frac{4}{9} & -2 \\ \hline \end{array} \]
02

Plot the points and graph the equation

Now, plot the coordinates in the table on a graph. To do this, locate the x-coordinate (-\frac{4}{9}) and then find the corresponding y-coordinates (5, 0, -1, -2) on the graph. Once the coordinates have been plotted, draw a vertical line passing through these points to represent the equation \(x = -\frac{4}{9}\). Since the equation defines a vertical line at x = -\frac{4}{9}, the line should be parallel to the y-axis.

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