Secton . — Ordered Pars, Intercepts, and Slopes
Model 3
Calculate the slope for the following equations:
Find two ordered pair
Equation
Calculate the slope
Validate
solutions
2x – y = 2
Let x = 1
Let x = 4
2 1
( )  =
y
2
y

y
2 4
( )  =
y
2
(
)
m
=
2
1
(
x

x
)
2
 =
y
2
 =
y
8
2
2
1
(
2 0

)
 =
y
0
 = 
y
2 8
m
=

(
2 1
)
y
=
0
 = 
y
6
2
Ordered pair 1 (1, 0)
y
=
6
slope
=
=
2
1
Ordered pair
(4, 6)
Let y = 2
2
x
 =
2 2
y

y
(
)
m
=
2
1
2
x
=
4
(
x

x
)
2
1
x
=
2
(
6 2

)
Ordered pair 2 (2, 2)
m
=

(
4 2
)
4
slope
=
=
2
2
Let x = 3
Let x = 1
y = 3x + 2
y
=
3
x
+
2
y
=
3 1
( )
+
2
(
y
−
y
)
m
=
2
1
(
x
x
)
y
=
3 3
( )
+
2
−
y
= +
3 2
2
1
(4 11)
−
y
= + =
9 2 11
y
=
5
m
=
2
Ordered pair 1 (3, 11)
Ordered pair
(1, 5)
−
3
3
Let y = 4
4 3
=
x
+
2
y
y
(

)
( 7)
−
m
=
2
1
m
=
(
x

x
)
4 3
=
x
+
2
2 9
2
1
−
(
5 11

)
2 3
=
x
3 3
m
=
(
1 3

)
x
=
3
2
( 7)
−
m
=
(

6
)
6
2
7
=
=
=
slope
3
x
=
−

(
2
)
2
3
3
7
3
2
−
−
, 4
Ordered pair 2
1
7
3
m
=
7
3
−
−
3
7
7
3
m
= −
−
1
7
21
slope
=
=
3
7
Though the mathematics for calculating the slope in the example above may seem overwhelming, remember that 1) it is
only mathematics and 2) you are free to choose the value you want to use for x as you solve for y. There is something of
an art to choosing values that keep fractions to a minimum; you will become increasingly skilled at this as you continue
to work through this chapter.