Create Equations with XY Tables

Create Equations from XY Tables - How it Works - Video

Example 1

Example 1:

First, we need to find a pattern in the XY table. Usually that involves finding the change in x and the change in y. The difference between each new x value is +1 and the difference between each new y value is +3. We have found our pattern.

We have the slope-intercept formula y = mx + b. Where m is the slope and b is the y-intercept. Luckily for us, we have the intercept at y = 11, which is the starting point, because x = 0.

Using the first point (0, 11), and substituting 0 for x and 11 for y, we get 11 = 11. Unfortunately, the m value goes away so this point doesn't work so we have to use the next point, (1, 14). After substituting 1 for x and 14 for y, we get 14 = m + 11. So m is to 3.

Another way to find m is to the rate of change. So the rate of change of y, +3, over the rate of change of x, +1, which is +3 / +1 and that is 3.

So our equation is y = 3x + 11.

Example 2

Example 2:

First, we need to find a pattern in the XY table. Usually that involves finding the change in x and the change in y. The difference between each new x value is +3 and the difference between each new y value is +6. We have found our pattern.

We have the slope-intercept formula y = mx + b. Where m is the slope and b is the y-intercept. Luckily for us, we have the intercept at y = 6, which is the starting point, because x = 0.

Using the first point (0, 6), and substituting 0 for x and 11 for y, we get 6 = 6. Unfortunately, the m value goes away so this point doesn't work so we have to use the next point, (3, 12). After substituting 1 for x and 12 for y, we get 6 = 3 * m. So m is to 2.

Another way to find m is to the rate of change. So the rate of change of y, +6, over the rate of change of x, +3, which is +6 / +3 and that is 2.

So our equation is y = 2x + 6.

Here we have the points in between 0 and 3 to show you why the rate works when there is pattern. Since we added the numbers in between, the difference between each new x value is +1 and the difference between each new y value is +2. We have found our pattern.

Once again to find m, we can use the rate of change. So the rate of change of y, +2, over the rate of change of x, +1, which is +2 / +1 and that is 2.

So our equation is still y = 2x + 6.

Live Worksheet

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