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Chapter 4: Problem 57

Complete the table of values for each equation, and plot the points. $$ \begin{aligned} &y=-4 x+3\\\ &\begin{array}{c|c} \hline x & y \\ \hline 0 & \\ \hline 2 & 0 \\ \hline & 7 \\ \hline \end{array} \end{aligned} $$

Short Answer

Expert verified
The completed table of values for the equation \(y = -4x + 3\) is: \[ \begin{array}{c|c} \hline x & y \\ \hline 0 & 3 \\ \hline 2 & 0 \\ \hline -1 & 7 \\ \hline \end{array} \] The points to plot on the graph are (0,3), (2,0), and (-1,7).

Step by step solution

01

Find the missing y value when x = 0

Plug x = 0 into the equation: \(y = -4(0) + 3\) \(y = 0 + 3\) \(y = 3\) So the table now has this value: \[ \begin{array}{c|c} \hline x & y \\ \hline 0 & 3 \\ \hline 2 & 0 \\ \hline & 7 \\ \hline \end{array} \]
02

Find the missing x value when y = 7

Plug y = 7 into the equation: \(7 = -4x + 3\) We want to isolate x, so move the terms around: \(-4x = 7 - 3\) \(-4x = 4\) Now, divide by -4 to solve for x: \(x = -1\) The table is now complete: \[ \begin{array}{c|c} \hline x & y \\ \hline 0 & 3 \\ \hline 2 & 0 \\ \hline -1 & 7 \\ \hline \end{array} \]
03

Plot the points on a graph

Using the completed table, we can now plot the points: 1. Point (0,3): Start at the origin (0,0), move 0 units horizontally and 3 units up, then plot the point. 2. Point (2,0): Start at the origin (0,0), move 2 units to the right and 0 units vertically, then plot the point. 3. Point (-1,7): Start at the origin (0,0), move 1 unit to the left and 7 units up, then plot the point. After plotting these points, you can now see the relationship between x and y for the equation \(y = -4x + 3\).

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