Luttrell 2012
85
Name: ______________________
Date: _____
6a – Linear Equations
Polynomials with
x
and y to the first power and are e
x
pressed either as A
x
+ By = C or
y = m
x
+ b are linear equations. They are called linear equations because when graphically
represented, the solutions form the shape of a line. There is a pattern between the solutions that
makes it easy to distinguish linear equations. In the spaces below, fill in the missing pieces to
the pattern:
Equations: A.
B.
C.
y
= 2
x
- 1
y
= -3
x
+ 2
2
x
+ 3
y
= 5
(-3, -7)
(0, 2)
(-5, 5)
(0, -1)
(1, -1)
(1, 1)
(3, 5)
(2, - 4)
(7, -3)
(6, 11)
(3, -7)
(13, -7)
In equation A, as
x
increased by___,
y
values increased by___. In equation B,
x
increased by___
each time
y
decreased by___. In equation C, increasing
x
by___ made
y
decrease by___.
It is necessary to find the solutions to a linear equation. Some people make a t-chart, where they
choose values of
x
(or
y
) and find the corresponding value of
y
(or
x
).
1. Fill in the t-chart for
x
- 2
y
= 6.
x
-2
1
2
y
-3.5 -3
-2
2. Fill in the t-chart for the following data: St. Joseph’s ice arena has a $3 admittance per person.
Let
x
represent the number of people in a group and y be the admittance price.
x
1
3
5
y
21
42
3. Let
x
represent a bag of apples that are being sold at $1.99 a bag. If
y
represents cost, fill in
the chart below:
x
4
12
y
11.94
19.90
