1. MSA 1.3: Using Linear Relationships
1) Learning Target: I can examine the pattern of change in a linear relationship.
2) MSA Inv 1 Day 3 Homework:
1) Complete pg. 9 for MSA 1.3 2) Correct online with the EDpuzzle
Warm Up: Find the unit rate and use it to write an equation relating the two quantities:
200 dollars for 50 t-shirts
70 dollars to rent 14 video games
12 tablespoons of sugar in 3 glasses of Cola
y = mx

2. Warm Up: Find the unit rate and use it to
Warm Up: Find the unit rate and use it to write an equation relating the two quantities:
200 dollars for 50 t-shirts
70 dollars to rent 14 video games
12 tablespoons of sugar in 3 glasses of Cola
y = mx
$200
50 shirts = X
1 shirt
x = $4 per shirt
200 = 4(50)
$70
14 videos = X
1 video
x = $5 per video
70 = 5(14)
12T.
3 glasses = X
1 glass
x = 4T. per glass of Cola
12 = 4(3)

3. 200 = 4(50) 70 = 5(14) 12 = 6(3) What is 200 dollars for 50 t-shirts
pkt. p. 7
What is
a dependent
variable?
an independent
variable?
WARM UP:
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 = 5(14)
70 dollars to rent 14 video games
The total amount spent ($70) is dependent
upon the number of video games rented at $5 each
12 = 6(3)
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

4. constant rate of change
independent variable
y = mx + b
dependent
variable
y-intercept
slope
constant rate of change
rate of change
coefficient

5. The class refers to these as pledge plans.
Tables, graphs, and equations will help predict how much money might be raised
with each plan.

6. What are the dependent (y) and the independent (x) variables?
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
Variable
Distance = X
Dependent
Variable
$ = y
What are
the dependent (y)
and
the independent (x)
variables?

7. As x goes up by 1, what happens to 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?
Dependent
Variable
$ = y
Independent
Variable
Distance = x
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

8. 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

9. B. Graph the three pledge plans on the same coordinate axes
B. Graph the three pledge plans on the same coordinate axes. Use a different color for each plan.
dependent variable
independent variable
x-axis
y-axis
KEY Alana
Gilberto
Leanne

10. As x goes up by 1, what happens to y?
For each pledge plan, what pattern of change between the
two variables do you observe in the graph?
In other words:
As x goes up by 1, what happens to y?
dependent variable
independent variable
x-axis
y-axis
Alana’s rate starts at $5 and increases with each km walked.
Gilberto’s rate starts at $0 and increases at a much faster rate than Alana.
Leanne starts at $10 and the rate doesn’t change.

11. 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?
Whose line are these points on? (10,10) (6,8)
Gilberto
Alana

12. C. For each pledge plan, write an equation that represents the relationship between the distance walked and the amount of money donated.
y = mx
Explain what information each number and variable in the equations represents.
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.

13. The pattern of change is the coefficient of x
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
Alana: y = 0.50x + 5
Gilberto: y = 2x
Leanne: y = 0x + 10
(the walking rate) (the independent variable)

14. Gilberto is proportional!
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.

15. In a table: as x increases by 1, y changes by a constant amount
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

16. MSA 1.3 Using Linear Relationships
Did I reach my Learning Target? I can examine the pattern of change in a linear relationship.
MSA Inv 1 Day 3 Homework:
1) Complete pg. 9 for MSA ) Correct online with the EDpuzzle.

17. Leanne: $10 per sponsor no matter how far she walks
MSA 1.3 HOMEWORK:
Alana: $ (8km) = $9
Gilberto: $2(8km) = $16
Leanne: $10 per sponsor no matter how far she walks

18. 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!

19. (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

20. Constant rate of change Amount subtracted for each t-shirt
y = mx + b
km walked
y = 2x – $4.75
Amount of $ Gilberto raises from each sponsor after he has paid for the T-shirt.
Constant rate of change $2
Amount subtracted for each t-shirt

21. 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.