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Chapter 4: Problem 3

Complete the table of values and graph each equation. $$ y=-2 x+4 $$$$ \begin{array}{c|c} x & y \\ \hline 0 & \\ \hline-1 & \\ \hline 2 & \\ \hline 3 & \\ \hline \end{array} $$

Short Answer

Expert verified
The completed table of values is: \(\begin{array}{c|c} x & y \\ \hline 0 & 4\\ \hline -1 & 6\\ \hline 2 & 0\\ \hline 3 & -2\\ \hline \end{array} \) After plotting the points (0, 4), (-1, 6), (2, 0), and (3, -2) on the coordinate plane, connect them with a straight line to graph the equation \(y=-2x+4\).

Step by step solution

01

Calculate y values for given x values

For each x value in the table, use the equation y = -2x + 4 to find the corresponding y values. Plug in each x value into the equation and solve for y.
02

Complete the table

Complete the table with the calculated y values: \(\begin{array}{c|c} x & y \\ \hline 0 & 4\\ \hline -1 & 6\\ \hline 2 & 0\\ \hline 3 & -2\\ \hline \end{array} \)
03

Plot the points on a graph

Now, plot the points from the table on a coordinate plane. Point 1: (0, 4) Point 2: (-1, 6) Point 3: (2, 0) Point 4: (3, -2)
04

Draw the line

Since this is a linear equation, the points will form a straight line. Connect the points with a straight line extending to the edges of the graph.
05

Label the graph

To finish the graph, label the x and y axis as well as the equation of the line, which is y = -2x + 4. Now you have successfully completed the table of values and graphed the equation y = -2x + 4.

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