The 'k' in Direct Variation
Find the hidden constant that links two changing quantities.
Equation
y = 2*x
Graph
Table
| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
What this lesson covers
What you do
You shape the function y = k*x and watch the graph answer.
Challenges to clear
- Find k if y = 12 when x = 4.
- Check with the same k: the line passes through (2, 6).
- This constant is a fraction, not a whole number. Its bottom is 4 — slide m there.
- Now the top: 12 must give 15. That makes k ÷ m = 5/4, and y ÷ x stays 5/4 on every row.
Check yourself
If y is directly proportional to x, and y = 10 when x = 2, what is y when x = 5?
In the equation y = kx, what does k represent?
- 25 — correct
- 50
- 15
- 10
- The ratio of y to x (y/x) — correct
- The product of y and x (y*x)
- The difference between y and x (y-x)
- A random constant that doesn't change
Think about it
- If y is directly proportional to x, what happens to y when x doubles?