1. Making an Equation from a Table (option 1) By: Mrs. Waters

2. 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.

3. Here is our table. Let’s start with the coefficient. XY -2-8 0-4 20 44 Is my table ready? Does my x’s go up by 1’s? +2 No! It doesn’t go up by 1.

4. Here is our table. Let’s start with the coefficient. XY -2 0 1 2 Now is it ready? Does my x’s go up by 1’s? +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 +2 -6-6 -2-2 Now, what is the pattern for one y? -8 -4-4 0

5. So, our coefficient is… 2 XY -2 0 1 2 +2 -6-6 -2-2 -8 -4-4 0 +1

6. 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

7. Let’s use x=0 to substitute. So…. Does y=0 when x=0? y = 2x XY -2-8 0-4 20 44 y = 2x y = 2(0)

8. XY -2-8 0-4 20 44 So, what do we need to make the equation work? y = 2x y = 2x+ (-4)

9. So, our equation is…. Now it’s your turn….. y = 2x+ (-4)

10. Find the equation for the given table. Click to the next slide to check your answer. XY -25 1 0-3 1-7

11. XY -25 1 0-3 1-7 -4 Another? Maybe with a graph?

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

13. XY -2-3 01 13