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LESSON 2.04:
Graphing Linear Relations using a Table of Values
MFM1P
Before we begin the lesson, evaluate each
equation using the given value.
(a) C= 4n + 20; when n = 3
(b) C = 25n + 220; when n = 50
(c) C = 2.5n + 30; when n = 17
Students will graph linear equations using a table.
A linear equation you can plug x vertically… Given an
equation that
y=_x or x=_y if you substitute values for
x or y, and plot a graph it will make a line!
The solution to linear equations are ordered pairs for you
to use on your graph!
What is a Linear Equation?
A linear equation is an
equation whose graph forms a
straight line.
Linear equations are usually
shown on a coordinate plane
AKA Cartesian Plane
Real life situations of linear
equations include the stock
market as well as the
payments of a car.
This is an example of a
linear equation
y=x+8
In this case whatever x is
plus 8 will give you the value
of y
Since the results of a linear equations
can be expressed as ordered pairs,
the linear equation can be graphed.
There are a number of ways to find
the solution to a linear equation…for
today’s lesson we will look at creating
a table of the solutions…
To create a table of solutions to a linear
equation do the following:
1. Choose a minimum of 3 values for x
2. Substitute the values of x into the linear
equation
3. Simplify to find the value of y
4. Write the solutions as ordered pairs
Let’s look at an example…
1. Choose a minimum
of 3 values for x
y = 2x – 1
x
0
y = 2x – 1
y = 2(0) – 1
y
-1
(x, y)
(0, - 1)
1
y = 2(1) – 1
1
(1, 1)
2
y = 2(2) – 1
3
(2, 3)
2. Substitute the value
of x into the equation
3. Simplify to
determine the
value of y
4. Write as an
ordered pair
How do you choose the value of x?
You can use any number for the value
of x…however, you can make your life
easy by choosing -1, 0, and 1, because
you can do mental math and they are
easy to graph.
You choose a minimum of 3 numbers
because when graphed the expected
result is a straight line. If you don’t get
the straight line, then you have to go
back and check your calculations…
x
0
1
2
Use the ordered pair from the table to graph the
linear equation.
Again…when graphing the result should be a
straight line…
Any point (ordered pair) on that line will be a
solution to the linear equation…
y
(2,3)
(1,1)
x
(0, -1)
(x, y)
(0, - 1)
(1, 1)
(2, 3)
1.
2.
3.
4.
Find 3 different ordered pairs that
are the solutions to the equation
y = 3x – 5
y = -2x – 6
y = ½ (4 – 2x)
y = 4( ½ x – 1)
Once you get the hang of it…this concept is really
easy….
However, like everything else to become
proficient you will need to practice…
It’s ok if you make a mistake…you can fix it…
The goal here is to keep an open mind and try…