Question

Use a table of values to graph the equation. $$ y=\frac{1}{2} x-5 $$

Short answer

The plotted points for the given equation \( y=\frac{1}{2} x-5 \) are (-2, -6),(-1, -5.5), (0, -5),(1, -4.5), (2, -4). Connecting these points gives the graph of the linear function.

Step-by-step solution

Choose Values for x

Choose at least two values for x to get at least two points to draw the line. It's usually a good idea to include 0, and a few positive and negative integers. Let's take, for instance, the values -2, -1, 0, 1, and 2.

Substitute x Values into the Equation

Consequently, substitute each of chosen x-values into \( y=\frac{1}{2} x-5 \) equation to compute the respective y-values. These are: when x=-2, \( y=\frac{1}{2}* -2-5 = -6 \); when x=-1, \( y=\frac{1}{2}*-1 -5 = -5.5 \); when x=0, \( y=\frac{1}{2}* 0 -5 = -5 \); when x=1, \( y=\frac{1}{2}*1 -5 = -4.5 \); when x=2, \( y=\frac{1}{2}*2 -5 = -4 \);

Plot the Coordinates on Graph

Now, this set of ordered pairs (-2, -6),(-1, -5.5), (0, -5),(1, -4.5), (2, -4) correspond to the coordinates that need to be plotted on the graph. Connect the points with a straight line because it's a linear function.