# Graphing Linear Equations and Using Slope Slopes and Intercepts

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"Graphing Linear Equations and Using Slope Slopes and Intercepts"

```					Graphing Linear Equations and Using Slope                                                                                            Lessons 12-1,12-2

Why? Many relationships can be represented by linear equations. The slope
of a linear graph is a measure of the rate of change of one variable
with respect to the other variable.

Graph linear equation y                                   2x     1.
y
x     y
4
(2, 5)                                                                      Positive    Negative
1      1                                                                                        y2      y1              slope       slope
rise
0      1                                                                   Slope
2                                                          run      x2      x1
2      5                          (0, 1)                  x
4     2 O          2            4
( 1,   1) 2                                                                                        Zero              Undefined
slope               slope
4

Slopes and Intercepts                                                                                                                         Lesson 12-3

Why? The slope-intercept form of an equation of a line
is often used to express a relationship.

Intercepts of a Line                                           Slope-Intercept Form of                            Standard Form of a
y                                                    a Linear Equation                                 Linear Equation
4      y-intercept = 2                                        Slope y-intercept                                Ax       By   C,
(0, 2)       x-intercept = 3                                                                               where A, B, and C
2
(3, 0) x                                      y      mx     b                                      are real numbers.
2 O        2     4                                       To graph a linear equation in                   To graph a linear equation in
2
this form, plot the y-intercept,                this form, ﬁnd the x-intercept
b, at (0, b). Then use the slope                and the y-intercept. Then plot
to ﬁnd a second point.                          and connect the two points.

Point-Slope Form                                                                                                                              Lesson 12-4

Why? The point-slope form of a linear equation
is convenient for some purposes.

Point-Slope Form of a                                                Write an equation of the line with
1
Linear Equation                                                   slope 2 that passes through point ( 3, 5).
y y1 m(x x1)                                                               y    y1     m(x     x1)
(x1, y1) is a point on the                                                               1
y    5      2
(x   ( 3))
line. m is the                                                                    1
y    5      2
(x   3)
slope of the line.

628B

```
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