Making an Equation from a Table (Option 2)

By: Mrs. Waters

Option 2 is finding the slope (or coefficient) using rise over run.

To do this, we will be finding the change in the y values and the

change in the x values.

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

X Y

-2 -8

0 -4

2 0

4 4

When we rise? What value changes?

The x value stays the same and the y value changes

When we run? What value changes?

The y value stays the same and the x value changes

Rise = Change in y values

So, what does that mean for rise over run?

Run = Change in x values

So, let’s find our coefficient (slope) by doing rise (change in y’s) over run (change in x’s)

X Y

-2 -8

0 -4

2 0

4 4

What is our change in y’s (rise)?

+2

+2

+2

Our run is 2

What is our change in x’s (run)?

+4

+4

+4

Our rise is 4

Rise = Change in y values = 4

So, our rise was 4 and our run was 4

Run = Change in x values = 2

So, our coefficient (or slope) = 2

=2

So, now we know our coefficient (slope) is 2.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 = 2x

y = 2xy = 2(0)

X Y

-2 -8

0 -4

2 0

4 4

X Y

-2 -8

0 -4

2 0

4 4

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

+ (-4)y = 2x

y = 2x

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