Step by step
The question
Question: write the equation for this table: x is 0, 1, 2, 3, and y is 2, 6, 10, 14.
x: 0, 1, 2, 3; y: 2, 6, 10, 14
We write it as a table.
1 Rate of change
Rate of change means: how much y changes when x goes up by 1.
y changes by 4 when x goes up by 1.
Change in y on top.
Change in x at the bottom.
= m = 41
m = change in y ÷ change in x
2 Start value
The start value is y when x is 0.
The table has x = 0: y is 2.
= b = 2
3 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 = 4x + 2.
= y = 4x + 2
4 Check
Let's check with the last pair: x = 3.
The equation gives 14.
The table says 14.
So the answer is right!
x = 3: 4 × 3 + 2 = 14
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
Answer
= y = 4x + 2