Moving Straight Ahead Investigation 1.3
Using Linear Relationships
Learning Target:
I can examine the pattern of change in a linear relationship.
Homework:
1) Complete pg. 9 for MSA 1.3
2) Correct online with the Zaption Review video.
Warm Up: Find the unit rate and use it to
write an equation relating the two quantities:
a) 200 dollars for 50 t-shirts
y = mx
b) 70 dollars to rent 14 video games
c) 12 tablespoons of sugar in 3 glasses of Cola
Warm Up: Find the unit rate and use it to
write an equation relating the two quantities:
y = mx
a) 200 dollars for 50 t-shirts
$200
X
=
50 shirts
1 shirt
x = $4 per shirt
200 = 4(50)
b) 70 dollars to rent 14 video games
$70
X
x = $5 per video
=
14 videos 1 video
70 = 5(14)
c) 12 tablespoons of sugar in 3 glasses of Cola
12T.
X
=
3 glasses
1 glass
x = 4T. per
glass of Cola
12 = 4(3)
Add Dependent Variable and Independent
Variable to your Vocabulary Toolkit
What is
WARM UP:
a dependent an independent
variable?
variable?
200 dollars for 50 t-shirts
200 = 4(50)
The total amount spent ($150) is dependent
upon the number of t-shirts at $4 each
70 dollars to rent 14 video games
70 = 5(14)
The total amount spent ($70) is dependent
upon the number of video games rented at $5 each
12 T. of sugar in 3 glasses of Cola
The total tablespoons of sugar (12T.) is dependent
upon the number of glasses of Cola at 4T. of sugar each
12 = 6(3)
independent variable
y = mx + b
dependent
variable
slope
constant rate of change
rate of change
coefficient
y-intercept
The class refers to these as pledge plans.
Tables, graphs, and equations
will help predict how much
money might be raised
with each plan.
Make a table for each student’s pledge plan. Show the amount of
money each of his or her sponsors would donate if he or she walked
distances from 0 to 6 kilometers.
Independent
What are
the dependent (y)
and
the independent (x)
variables?
Variable
Distance = X
Dependent
Variable
$=y
For each pledge plan, what pattern of change between the
two variables do you observe in the table?
In other words:
As x goes up by 1,
what happens to y?
Alana:
as (x) increases by 1 km,
(y) increases by $0.50
Gilberto:
as (x) increases by 1 km,
(y) increases by $2
Leanne:
as (x) increases by 1 km,
(y) has no change
Independent
Variable
Distance = x
Dependent
Variable
$=y
FYI:
(For Your Information)
What is the starting point
for each student?
This is also called the
y-intercept.
What is the rate of change
for each student?
This is also called the slope.
Independent
Variable
Distance = X
Dependent
Variable
$=Y
B. Graph the three pledge plans on the same coordinate axes.
Use a different color for each plan.
y-axis
dependent variable
KEY
Alana
Gilberto
Leanne
x-axis
independent variable
For each pledge plan, what pattern of change between the
two variables do you observe in the graph?
In other words:
y-axis
Gilberto’s rate starts at $0
and increases at a much
faster rate than Alana.
x-axis
Alana’s rate starts at $5
and increases with each
km walked.
dependent variable
As x goes up by 1,
what happens to y?
Leanne starts at $10 and
the rate doesn’t change.
independent variable
FYI:
(For Your Information)
What is the starting point for
each student?
This is called the y-intercept.
What is the rate of change for
each student?
This is called the slope.
What does the point (6,12)
represent? Whose line is it
on?
Gilberto
Whose line are these points
on? (10,10) (6,8) Alana
C. For each pledge plan, write an equation that represents the
relationship between the distance walked and the amount of money
donated.
Explain what information each
number and variable in the
equations represents.
y = mx
Alana: y = 0.50x + 5
Gilberto: y = 2x
or y = 2x + 0
Leanne: y = 0x + 10
or y = 10
y = money earned in dollars
(dependent variable)
x = distance walked in km
(independent variable)
The coefficient (the number
in front of the variable)
represents the walking rate.
For each pledge plan, what pattern of change between
the two variables do you observe in the equation?
The pattern of change is
the coefficient of x
(the walking rate)
Alana: y = 0.50x + 5
Gilberto: y = 2x
Leanne: y = 0x + 10
(the independent variable)
D. Does each pledge plan represent a
proportional relationship?
Alana: y = 0.50x + 5
Gilberto: y = 2x
or y = 2x + 0
Leanne: y = 0x + 10
or y = 10
The relationship between money and distance walked for…
Gilberto is proportional!
It is NOT proportional for Leanne and Alana because sponsors
donate an initial amount in addition to money donated per kilometer.
This makes the ratio of money donated to kilometers walked not a
constant.
E. How can you determine if a relationship is linear from a
table, a graph, or an equation?
In a table:
as x increases by 1,
y changes by a constant amount
In a graph:
there is a straight line
In an equation:
it follows the formula of y = mx + b
MSA 1.3
Walking Rates & Linear Relationships
Did I reach my Learning Target?
I can examine the pattern of change in a linear relationship.
Homework:
1) Complete pg. 9 for MSA 1.3
2) Correct online with the Zaption Review video.
MSA 1.3 HOMEWORK:
Alana: $5 + 0.5(8km) = $9
Gilberto:
$2(8km) = $16
Leanne: $10 per sponsor no matter how far she walks
Alana: $5 + 0.5(?km) = $10, so 0.5 x 10 km = 5
Gilberto: $2 x ? km = $10, so 10/2 = 5 km
Leanne: Can’t determine!
(12, 11) lies on Alana’s graph.
If Alana walks 12km, each sponsor donates $11.
When her distance is zero, she already has $5
(0, 5) it is the starting point, or y-intercept!
5 is the term added to 0.5x
y = mx + b
Amount of $
Gilberto raises from
each sponsor after
he has paid for the
T-shirt.
km walked
y = 2x – $4.75
Constant rate
of change
$2
Amount
subtracted for
each t-shirt
• This graph starts at (0, -4.75), the
other was (0,0)
• Both graphs have the same steepness
(slope).
• For every value of x, the y-coordinate
of a point on this graph is exactly 4.75
less than the y-coordinate on the
other graph.
• Yes, it is linear. There is a constant rate
of change, and it is a straight line.