Question

Use a table of values to graph the equation. $$y=3 x-1$$

Short answer

The plotted points based on the table of values are (-1, -4), (0, -1), and (1, 2). These points form a straight line when plotted on a graph, which is the graph of the equation \(y = 3x -1\).

Step-by-step solution

Prepare the table of values

To create a table of values for the equation, select three or more values for \(x\). An easy choice is to pick -1, 0, and 1 for \(x\). This part of the process is subjective. Any value for \(x\) will work with this equation.

Fill the table of values

Now, substitute these \(x\) values into the equation \(y = 3x - 1\) to get the corresponding \(y\) values. The resulting pairs \((x,y)\) are (-1, -4), (0, -1), and (1, 2).

Draw the graph

Plot these \(x, y\) value pairs as points on a graph. After that, draw a straight line through these points to represent the equation.

Checking

In order to ensure correctness, make sure that all points lie along the same line. If they do, then you've graphed the equation correctly.