Question

Use a table of values to graph the equation. $$y=x-7$$

Short answer

The graph of the equation \(y=x-7\) is a straight line that passes through the points (-2,-9), (0,-7), (2,-5), (4,-3), and (6,-1). It has a slope of 1 and crosses the y-axis at y=-7.

Step-by-step solution

Setting up the table of values

Choose five values for x. The values can be arbitrary, but it's often useful to include negative, zero, and positive values. For this exercise let's use -2, 0, 2, 4, and 6. Then, apply these values into the equation to find the corresponding y-values.

Calculating y-values

Now, substitute each chosen x-value into the equation and solve for y. For example, when x=-2, \(y=-2-7=-9\). Repeat for each x-values. The result should be this table: \n\n|x | y |\n|--- |--- |\n|-2 |-9|\n|0|-7 |\n|2|-5 |\n|4|-3|\n|6|-1|

Plotting the points

Each (x, y) pair represents a point in a two-dimensional space. So, for each pair, put a point in the corresponding position on the coordinate grid. In the end, there should be five points.

Drawing the graph

Finally, connect all the points with a straight line to complete the graph of the equation \(y=x-7\). The line should cross through all five points, showing a linear relationship between x and y.