Making an Equation from a Table (option 1)

By: Mrs. Waters

Option 1 is finding the slope (or coefficient) by finding the unit rate. To do this, we will change the table so that each x goes up by one. Then, we will see how much y increases for 1 x.

Here is our table. Let’s start with the coefficient.

X Y

-2 -8

0 -4

2 0

4 4

Is my table ready?Does my x’s go up by 1’s?

+2

+2

+2

No! It doesn’t go up by 1.

Here is our table. Let’s start with the coefficient.

X Y

-2

-1

0

1

2

Now is it ready?Does my x’s go up by 1’s?

+1

+1

+1

Fill in the y’s you know. What is the pattern? Once you know, fill in the blanks.

Now it does! Let’s find the pattern in y for one x.

They go up by 4 for two x’s. So, for one x it goes up by 2.

+1

+4

+4

+2

+2

+2

+2

-6

-2

Now, what is the pattern for one y?

-8

-4

0

So, our coefficient is… 2X Y

-2

-1

0

1

2

+2

+2

+2

+2

-6

-2

-8

-4

0

+1

+1

+1

+1

So, now we know our coefficient is 3 let’s put it in the equation.

But does this equation work for our table?

Let’s find out by SUBSTITUTING! YAY!

y = 2x

Let’s use x=0 to substitute.So….

Does y=0 when x=0?

y = 2xX Y

-2 -8

0 -4

2 0

4 4

y = 2xy = 2(0)

X Y

-2 -8

0 -4

2 0

4 4

So, what do we need to make the equation work?

y = 2x

y = 2x+ (-4)

So, our equation is….

Now it’s your turn…..

y = 2x+ (-4)

Find the equation for the given table. Click to the next slide to check your answer.

X Y

-2 5

-1 1

0 -3

1 -7

X Y

-2 5

-1 1

0 -3

1 -7-4

-4

-4

Another? Maybe with a graph?

Create an equation from the GraphFind the points on the graph to make a table.Click to the next slide to check your answer.

X Y

-2 -3

-1 -1

0 1

1 3