Grade 7 Mathematics
A PROPORTIONAL RELATIONSHIP exists when two quantities have a constant ratio. This constant is called k (the constant of proportionality).
The equation is always: y = kx
The graph ALWAYS passes through the ORIGIN (0, 0)!
TABLE: Every y/x gives the SAME value (k)
GRAPH: Straight line through (0, 0)
EQUATION: y = kx (no number added or subtracted)
A babysitter earns money based on hours worked:
| Hours (x) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Earnings (y) | $15 | $30 | $45 | $60 |
Calculate y/x for EACH column: 15/1 = 15, 30/2 = 15, 45/3 = 15, 60/4 = 15
All values are the SAME! So this IS proportional. k = 15
Write the equation: y = 15x (earnings = $15 times hours)
What does k mean? k = 15 means the babysitter earns $15 PER HOUR (unit rate!)
Using the same table, let's graph the relationship:
Key Points to Plot:
(0, 0), (1, 15), (2, 30), (3, 45), (4, 60)
Notice: The line passes through (0, 0)!
WRONG: "If it's a straight line, it's proportional."
RIGHT: A proportional graph must be a straight line that passes through the ORIGIN (0, 0). If the line crosses the y-axis anywhere else, it's NOT proportional! Example: y = 2x + 3 is linear but NOT proportional because it crosses at (0, 3).
Is this relationship proportional?
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 5 | 8 | 11 | 14 |
| y/x | 5 | 4 | 3.67 | 3.5 |
NOT proportional! The ratios are NOT equal. (Also: the equation is y = 3x + 2, which has "+2")
1. Is this relationship proportional? Find k if it is.
| x | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| y | 10 | 20 | 30 | 40 |
Proportional? k = Equation: y =
2. A car travels at a constant speed. It goes 180 miles in 3 hours.
a) What is the constant of proportionality (k)?
b) Write the equation: y =
c) How far will the car travel in 5 hours?
3. Which equation represents a proportional relationship? Circle all that apply.
A) y = 4x B) y = 3x + 1 C) y = x/2 D) y = 5 E) y = 0.5x
4. The graph of a proportional relationship passes through (4, 12). Find k and write the equation.
k = y/x = Equation: y =