Step by step
The question
Question: write the equation for this table: x is 1, 2, 3, 4, and y is 7, 11, 15, 19.
We write it as a table.
There are four choices.
First we solve it, the normal way.
Then we pick.
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.
That is the rule for m.
2 Start value
The start value is y when x is 0.
The table starts at x = 1.
We go back from x = 1 to x = 0: one step of 1.
Each step, take away 4.
7 minus 4 is 3.
So y at 0 is 3.
Careful!
7 is y at x = 1.
The start value is y at x = 0.
3 Write the equation
A line is y = m x plus b: m is the rate of change, b is the start value.
So the equation is y = 4x + 3.
4 Check
Let's check with the last pair: x = 4.
The equation gives 19.
The table says 19.
So the answer is right!
5 Pick the choice
Our answer is y = 4x + 3.
That is choice C.
6 Why not the others
A is y = x + 6.
Wrong: the rate is how much y grows each time x grows by 1: 4, not 1.
B is y = 3x + 4.
Wrong: the start and the rate swapped.
D is y = 4x + 7.
Wrong: 7 is y at x = 1: the start is y at x = 0.
That is the Careful mistake from before.
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Then: check.
Then: pick the choice.
Last: why not the others.