Proportional Relationships
Rate of Change
Slope of Graphs
Slope of Points
Throwback
100
We use this letter to represent proportional relationships, known as The Constant of Proportionality.
k
100
Rate of change is represented by the change in ___ over the change in ___ (labels included).
Change in y/Change in x
100
What are the 4 types of slope we've discussed in class?
1. Positive
2. Negative
3. Zero
4. Undefined
100
What is the slope formula?
m = y2 - y1 / x2 - x1
100
Solve!
2a = 8
a = 4
200
After finding the Constant of Proportionality, the equation of a proportional relationship can be written in this form.
y = kx
200
DAILY DOUBLE
We use this symbol to represent change.
Δ Delta
200
What type of slope does this graph represent?
Positive
200
Find the slope between the two points.
(1, 5) and (10, 4)
m = -1/9
200
Solve!
3p + 10 = 40
p = 10
300
What is the Constant of Proportionality of the following equation?
x | 2 | 3 | 8 | 10 |
y | 4 | 6 | 16 | 20 |
y = 2x
300
What is the rate of change of the table below?
Time (hrs) | 2 | 5 | 10 |
Burgers | 10 | 25 | 50 |
5 burgers per hour
300
What type of slope does this graph represent?
Negative
300
Find the slope between the two points.
(-8, 12) and (-16, -20)
m = 4/1
300
What are the two methods we've discussed in solving systems of equations?
Elimination and Substitution
400
What are the two characteristics that make up a proportional graph?
1. A straight line
2. The line crosses the origin (0, 0)
400
Burt is renting a van. It costs $160 for 4 hours and $320 for 6 hours. What is the rate of change for this situation?
$80/hr
400
What is the type of slope represented by this graph?
Zero
400
If the slope of a line is 3, what is the missing coordinate?
(4, 10) and (7, y)
y = 19
400
Solve!
−5(x + 2) = −(−5x + 1) − x
x = -1
500
These three concepts are the same, the only difference is that one has a label.
- Slope
- Constant of Proportionality
- Rate of Change/Unit Rate
500
Tank A is being filled with soup at a rate of 3 gallons per hour. Tank B is being filled with soup as well, and can be represented by the equation y = 5x, which tank is being filled faster?
Tank B
500
What is the slope of the line?
m = 5/3
500
If the slope of a line is -1/7, what is the missing coordinate?
(x, 21) and (19, 28)
x = 20
500
Solve the system:
−4x − 2y = −12
4x + 8y = −24
(6, -6)