Algebra Know-It-ALL

where a and b are constants. If you substitute y for 0 and then transpose the left and right
sides, you get an equation for a linear function where y is the dependent variable and x is the
independent variable:

y=ax+b

As things work out, the constant a is the slope of the graph, and the constant b is the y-intercept.
Because the slope is usually symbolized by m instead of a, you can write

y=mx+b

This is the classical expression of the SI form for a linear function.

Are you confused?

If the graph of a linear relation is a vertical line, then the slope is undefined, and the relation is not a func-
tion. The graph of a linear function must be a nonvertical line; otherwise it would fail the vertical-line test
in the worst possible way! Whenever you see a linear relation that simply says x is equal to some constant,
then you know that relation is not a function of x. Figure 15-3 shows some examples. Note that all the
lines are vertical; they are parallel to the dependent-variable axis.

–6 246

2

4

6

–2

–4

–6

x

y

–4 –2

y-intercept is 3

y-intercept is –2 Slope is

negative

Slope is

positive

Figure 15-2 Two examples of y-intercept points for

straight lines. The line that ramps upward

as we move to the right has positive slope;

the line that ramps downward as we move

to the right has negative slope.

Slope-Intercept Form 239