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Question 236882: I don't understand how to write the rule for a table when it is x squared.
x Y
1 9
2 12
3 17
4 24
I know the answer is y=x^2+8, but I don't know how to get that answer.
Thanks
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! Your table:
x.......... y
1............9
2............12
3............17
4............24
You are given an equation.
When you plug the given values for x, you get the corresponding y values as shown on the table.
For example, when x = 1, y = (1)^2 + 8 = 1 + 8 = 9.
So, when x = 1, y = 9.
Do you understand?
The table reveals the y values when you plug the given x values and simplify.
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I got your reply. You said:
"Is there a formula to follow if I didn't know the answer was y = x^2 + 8 because if I take the change in y divided by the change in x and use the equation of a line y = mx + b, I don't get the right answer."
The change in y divided by the change in x leads to the slope of the line.
You did not say anything about slope in your original question.
The equation y = x^2 + 8 is not in slope form. This equation is actually a parabola. The only thing I can see from the information you provided is that a table or chart was needed to form an equation. The equation y = x^2 + 8, when plugging the given x values, gave you 4 different y values. See it?
One thing to be noted here is the fact that each x and y value creates a point in the form (x, y).
Here is an example:
From your table, when x = 1, y = 9. This makes the point (1, 9).
From your table again, when x = 2, y = 12 making the point (2, 12).
You can continue this pattern to find other 2 points as well.
Once you find all 4 points, you can then use those points to find the slope of the line.
Let m = slope
m = difference in y values divided by difference in x values
This is the only thing I can see where the table information leads to the slope of the line. In reality, based on the fact that four x values and four y values appear on this table, we can find two slopes using the slope formula above.
Is this clear?
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