Step by step
The question
Question: Ana has $10 and saves $5 per week.
Write the equation.
1 Which depends on which
The money depends on the number of weeks.
So x is the weeks: the input.
y is the money: the output.
x = weeks, y = money
2 Rate of change
Rate of change means: how much y changes when x goes up by 1.
Each week, it goes up by 5.
So m is 5.
= m = 5
3 Start value
The start value is y when x is 0.
At the start, with 0 weeks, it is 10.
= b = 10
Careful!
The 5 is per week: it goes with x.
The 10 is only once.
Careful: not y = 10x + 5 ✗
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 = 5x + 10.
= y = 5x + 10
5 Check
Let's check with 4 weeks: the equation gives 30.
In the story: 10, plus 5, plus 5, plus 5, plus 5: 30.
So the answer is right!
x = 4: 5 × 4 + 10 = 30
Let's look back.
First: which depends on which.
Then: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = 5x + 10