Algebra Know-It-ALL

240 Graphs of Linear Relations

Here’s a challenge!

Put the following equation into SI form as a linear function of x, and graph it on that basis:

8 x+ 4 y= 12

Solution

We must rearrange this equation to get y all by itself on the left side of the equality symbol, and an

expression containing only x and one or more constants on the right side. Subtracting 8x from both sides

gives us

4 y=− 8 x+ 12

Dividing each side by 4 puts it into SI form:

y= (− 8 x)/4+ 12/4

=− 2 x+ 3

The slope is −2, and the y-intercept is 3. Figure 15-4 shows the graphing process. We plot the y-intercept

point on the y axis at the mark for 3 units. That gives us a point with coordinates (0, 3). To plot the line,

–6 246

2

4

6

–2

–4

–6

x

y

–4 –2

x= –5 x= 3/2 x= 5.78

Figure 15-3 These linear relations are not functions of x.

The slopes of the graphs are undefined,

because they are all straight lines parallel to

they axis.