Step by step
The question
Question: A taxi costs $3 plus $2 per mile.
Write the equation.
1 Which depends on which
The cost depends on the number of miles.
So x is the miles: the input.
y is the cost: the output.
x = miles, y = cost
2 Rate of change
Rate of change means: how much y changes when x goes up by 1.
Each mile, it goes up by 2.
So m is 2.
= m = 2
3 Start value
The start value is y when x is 0.
At the start, with 0 miles, it is 3.
= b = 3
Careful!
The 2 is per mile: it goes with x.
The 3 is only once.
Careful: not y = 3x + 2 ✗
4 Write the equation
A line is y = m x plus b: m is the rate of change, b is the start value.
y = mx + b
So the equation is y = 2x + 3.
= y = 2x + 3
5 Check
Let's check with 4 miles: the equation gives 11.
In the story: 3, plus 2, plus 2, plus 2, plus 2: 11.
So the answer is right!
x = 4: 2 × 4 + 3 = 11
Let's look back.
First: which depends on which.
Then: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = 2x + 3