Question

Use a table of values to graph the equation. \(y=-3 x+1\)

Short answer

The table of values is \[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & 7 \\ \hline -1 & 4 \\ \hline 0 & 1 \\ \hline 1 & -2 \\ \hline 2 & -5 \\ \hline \end{array} \] and the line passes through the points \((-2, 7)\), \((-1, 4)\), \((0, 1)\), \((1, -2)\), and \((2, -5)\).

Step-by-step solution

Choose Appropriate Values for \(x\)

Evaluate the equation for a range of \(x\)-values. For simplicity, we can start with \(x = -2, -1, 0, 1, 2\).

Calculate Corresponding \(y\)-Values

Plug in each value of \(x\) in the equation \(y=-3 x+1\) to find the corresponding \(y\)-values. For example, if \(x = -2\), \(y = -3(-2) + 1 = 7\). Similarly, calculate \(y\) for all chosen \(x\) values.

Form a Table of Values

The table of values from our calculations would look like this: \[ \begin{array}{|c|c|} \hline x & y \\ \hline -2 & 7 \\ \hline -1 & 4 \\ \hline 0 & 1 \\ \hline 1 & -2 \\ \hline 2 & -5 \\ \hline \end{array} \]

Plot the Points on the Graph

Plot the points (\(x, y\)) from the table on a coordinate plane. The points are \((-2, 7)\), \((-1, 4)\), \((0, 1)\), \((1, -2)\), and \((2, -5)\).

Draw the Line

Draw a line through all the plotted points. This is the graph of the given equation \(y = -3x + 1\).