Download 4.4 - Matching Equations and Graphs(2).

4.4 – Matching Equations and
Graphs
Math 9
3 students participate in a 5-km walk for charity. Each
student has a different plan to raise money from his/her
sponsors. These graphs show how the amount of money a
sponsor owes related to the distance walked.
Match each graph with its equation
y
y
y
25
12
12
Monica
Sari
Bruce
5
2
2
1
m  2d  3
5
x
x
x
1
5
m  4d
1
m d 5
Describe, in words, each person’s sponsorship plans.
5
Example 1: The 3 graphs on your handout have these
equations, but the graphs are not in order. Match each
equation with its graph.
y  3x  3
xy 3
y  3x  3
Let’s get the equations to all follow the same format. (y=)
What is the same
about these equations,
what is different?
What else do you
need to
determine what a
graph looks like?
Let’s complete a table of values for each equation.
y = 3x + 3
x
0
1
2
y
y=3–x
x
0
1
2
y
y = 3x – 3
x
y
0
1
2
So, to match each equation with its graph, use the
equation to determine 3 points. Then find out which
graph passes through those 3 points.
y = 3x – 3
y = 3x + 3
y=3–x
Is there any way you
can use the equation
to determine what the
graph looks like?
Match each graph on the grid with the equation...
y
y=x
8
y = 2x
y = -3x
x
-8
8
We can match the
equation to the graph
by looking at the
coefficient of x.
-8
Match each graph on the grid with the equation cont…
y=x
What is the coefficient
for each of these
equations?
y = 2x
y = -3x
Remember, for each
equation we’ve
created before, the
coefficient describes
what happens to y
when the x-value
increases by 1.
A coefficient of 1 means that when x increases by 1 unit, y
also increases by 1 unit.
 A coefficient of 2 means that when x increases by 1 unit, y
increases by 2 units.
 A coefficient of -3 tells us that y decreases by 3 units when
x increases by 1 unit.
y = -3x
y
y=x
8
y = 2x
x
-8
8
-8
Note… The coefficient of the x term, when written as above,
is more commonly referred to as the slope of the equation.
Identifying a Graph Given its Equation
y
6
Which graph on this grid has
the equation y = 3x – 4?
Justify your answer.
x
-4
4
To solve this problem, pick 2
points on each graph and
check to see if they satisfy
the equation.
Remember to evaluate the
left side and right side
independently.
-6
Assignment
Time
Pg. 188-190
#3-9, 11c, 13