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THE PICTURE OF MATH
Making equations visible
TWO VARIABLE EQUATIONS
One variable equations have exactly one answer.
2 𝑥 + 4 = 4𝑥 − 2
2𝑥 + 8 = 4𝑥 − 2
8 = 2𝑥 − 2
10 = 2𝑥
5=𝑥
given
distributive property
subtraction prop (=)
addition prop (=)
division prop (=)
TWO VARIABLE EQUATIONS
But two variable equations contain infinite possible
combinations of answers.
X
Y = 2X - 3
Y
-1
Y = 2(-1) – 3
-5
0
Y = 2(0) - 3
-3
1
Y = 2(1) – 3
-1
2
Y = 2(2) - 3
1
TWO VARIABLE EQUATIONS
A two variable equation is like a machine.
You put in a value for one of the variables and get out a value
for the other variable
TWO VARIABLE EQUATIONS
These values combine
together to create
Ordered pairs,
(-1, -5)
( 0, -3)
( 1, -1)
( 2, 1)
which can be plotted on the
Coordinate plane.
TWO VARIABLE EQUATIONS
But, are these all the possible answers?
How many possible answers are there?
Infinitely many possible answers exists.
And not just integers, but fractions and
Irrational numbers as well.
So, to show all possible answers we
Need to make a continuous graph.
YOUR TURN
On grid paper show all possible solutions for y = 3x
First, find ordered pairs by entering values for one variable and
solve to find the other variable.
Then, graph these ordered pairs.
Finally, create a line or curve to fit the points.
DID THAT LAST SLIDE SAY
CURVE?
Yes. Not all equations make straight lines.
𝒚= 𝒙−𝟐
𝑦 = 𝑥2
𝑦 = 2𝑥
HOW DO WE KNOW WHAT AN
EQUATION WILL LOOK LIKE?
There are clues in the equations themselves that we’ll learn later,
But for now you need find several ordered pairs to graph.
Also make sure you choose some negative input values as well
as zero and positive input values.