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