Luttrell 2012
86
Name: ______________________
Date: _____
6b – Graphs of Linear Equations
Some of the solutions to 2
x
-
y
= 1 are (-2,-5), (0,-1), and (1, 1). Recognizing 2
x
-y = 1 as a linear
equation, the conclusion can be made that there is a pattern between the ordered pairs. Between
the first two pairs,
x
increases by 2. But between the last two pairs, it increases by 1. With such
inconsistency, it will give some difficulty for writing an equation when only given coordinates.
So to circumvent this problem, slope was defined. Slope is the ratio of the change between y-
values to the change between
x
-values. As any ratio can be reduced to simplest terms, the ratio
4/2 between the first two ordered pairs reduces to 2, which is the ratio between the last two pairs.
Algebraically, slope (
m
) is defined as
m
y
y
x
x
=
−
−
1
2
1
2
. Other e
x
pressions are
rise
run
y
x
=
∆
∆
.
Slope can be found by taking the ratio between two ordered pairs, or by looking at the equation
when it is in the form
y = mx + b
(slope-intercept form). Solving for
y
in the e
x
ample gives
y = 2
x
- 1. If
x
= 0, the equation gives y = -1, just like the -1 in the equation. The y-intercept (b)
is represented by the -1. Go ahead and plot the point on the graph. By evaluating more values of
x
, more ordered pairs are obtained: (1,1) and (2, 3). The same can be done by starting at the
y
-
intercept and moving right 1 and up 2 and make a dot. Notice the slope was 2 and there is a
x
-
coefficient of 2 in the equation. So graphing can be done by knowing your
m
’s and
b
’s.
Graph the following:
1. 2
x
+
y
= 3
2. 6
x
+ 2
y
= 4
3. -6
x
+ 3
y
= 9
4.
y
=
x
- 3
5.
y
= 5
x
- 2
6.
y
= (½)
x
- 3
7.
y
= -2
x
+ 1
8. -
x
-
y
= 3
9.
y
= 3
x
