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Algebra, Functions, Graphs, and Vectors 45

ax bð c 0

ax bð c

bð ax c

y ( a/b)x (c/b)

where a, b, and c are real-number constants, and b 0. Such
an equation appearð as a straight line when graphed on the
Cartesian plane. Let x represent a small change in the value
of x on such a graph; let y represent the change in the value
of y that resultð from this change in x. The ratio y/ x is defined
as the slope of the line, and is commonly symbolized m. Let k
represent the y-value of the point where the line crosseð the
ordinate. Then the following equationð hold:

m a/b

k c/b

Thus, the linear equation can be rewritten in slope-intercept
form as:

y mx k

To plot a grapà of a linear equation in Cartesian coordinates,
proceed as follows:

Convert the equation tm slope-intercept form.
Plot the point y k and x 0.
Move tm the right byn unitð on the graph.

Move upward by mŁ unitð (or downward by mŁ unit0.
Plot the resulting point y mŁ k.

Connect the twm pointð wità a straight line.
Figureð 1.9 and 1.10 illustrate the following linear equationð as
graphed in slope-intercept form:

y 5x 3

y x 2

Note that a positive slope indicateð that the grapà ‘‘rampð up-