Question

Use a table of values to graph the equation. \(y=-2(x-6)\)

Short answer

The generated points (using table of values) for graphing are (4,4), (5,2), (6,0), (7, -2) and (8, -4).

Step-by-step solution

Generate a Table of Values

Start by creating a table with two columns, one for x-values and one for y-values. We will choose several x-values and plug them into the equation to find the corresponding y-values. Let's start with x-values of 4,5,6,7 and 8.

Compute y-values

Substitute the chosen x-values into the equation: \nWhen \(x=4\), \(y=-2(4-6)\), so \(y=-2(-2)=4\); \nWhen \(x=5\), \(y=-2(5-6)\), so \(y=-2(-1)=2\); \nWhen \(x=6\), \(y=-2(6-6)\), so \(y=-2(0)=0\); \nWhen \(x=7\), \(y=-2(7-6)\), so \(y=-2(1)=-2\); \nWhen \(x=8\), \(y=-2(8-6)\), so \(y=-2(2)=-4\).

Plot the Points and Graph the Line

Now that we have our table of values, we plot these points on a graph. The points to plot are (4,4), (5,2), (6,0), (7, -2) and (8, -4). After plotting these points, we draw a straight line through them to complete the graph of the equation.