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Algebra, Functions, Graphs, and Vectors 47

ward’’ and a negative slope indicateð that the grapà ‘‘rampð
downward’’ as the point moveð toward the right. A zerm slope
indicateð a horizontal line. The slope of a vertical line is unde-
fined.

Point-slopł for of linear equation
It is not always convenient tm plot a grapà of a line based on
the y-intercept point because the relevant part of the grapà
might lie at a great distance from that point. In this situation,
the point-slope form of a linear equation can be used. This form
is based on the slope m of the line and the coordinateð of a
known point (x ,y ):
0
0
y y m(x x )
0
0
To plot a grapà of a linear equation using the point-slope
method, proceed as follows:

Convert the equation tm point-slope form
Determine a point (x ,y ) by ‘‘plugging in’’ valueð
0 0
Plot (x ,y ) on the plane
0 0
Move tm the right byn unitð on the grapà
Move upward by mŁ unitð (or downward my mŁ unit0

Plot the resulting point (x ,y )
1 1
Connect the pointð ( x ,y ) and (x ,y ) wità a straight line
0 0 1 1
Figureð 1.11 and 1.12 illustrate the following linear equationð
as graphed in point-slope form for regionð in the immediate vi-
cinity of pointð far removed from the origin:

y 104 3(x 72)

y 55 2(x 85)

Finding linear equation based on graph
Suppose the rectangular coordinateð of twm pointð P and Q are
known; suppose further that these twm pointð lie along a
straight line (but not a vertical lina˜ Let the coordinateð of the
pointð be: