At £3 an hour, the money earned depends on the hours worked. Hours is the independent variable.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The rule
m = 3h. Choose any h, and the rule gives you m.
The same rule as a table
1 hour gives 3, 2 hours give 6, 3 hours give 9.
And as a graph
Each pair is a point. Plotted together they fall in a straight line through the origin.
Independent and dependent
In y = 3x, you choose x and y follows. The one you choose is independent; the one that follows is dependent. Deciding which is which comes from the situation, not from the letters — hours worked determine pay, not the reverse.
A table of matching values
For y = 3x: when x is 1, y is 3; when x is 2, y is 6; when x is 5, y is 15. A table records the relationship as a set of pairs, and those pairs are exactly what you plot on the coordinate plane.
The graph shows the relationship
Plotting those pairs gives points on a straight line through the origin. The equation, the table and the graph are three views of one relationship. Being able to move between them is one of the main goals of middle school algebra.
Reading a relationship from a situation
If a taxi charges £3 per mile, then cost = 3 × miles, so c = 3m. Recognising a proportional relationship in words and writing it as an equation is the skill that carries into every later modelling problem.
Step 2: Try It Yourself
Move the point and read the pair it stands for.
Go 3 across, then 9 up. The first number is always the across one.
Step 3: Watch an Example
One step at a time.
Watch Ana Fill a Table
A taxi charges £2 per mile. Ana works out the fare for several distances.
- Step 1
She decides which depends on which: the fare depends on the miles.
Step 4: Your Turn
Practice makes it stick.
The Taxi
Problem 1 of 2
At £2 a mile, what is the fare for 7 miles, in pounds?
Working Backwards
Problem 2 of 2
At £2 a mile, a fare of £18 covers how many miles?
Follow the Rule
1 of 4
If m = 3h, what is m when h is 5?
2 of 4
If m = 3h, what is h when m is 21?
3 of 4
In "money earned depends on hours worked", which is independent?
4 of 4
If y = 4x, what is y when x is 6?
Step 5: Quick Check
Show what you know.
Question 1 of 1
If y = 5x, what is y when x is 8?
What You Learned
- The independent variable is the one you choose; the dependent one follows.
- A rule can be written as an equation, a table, or a graph.
- All three say the same thing, so any one can be built from another.