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Question 179854: When you have a t-table with the x's as 0,1,2 and the y's as 17,23,29..
what is the equation?
Found 2 solutions by Mathtut, solver91311:
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! you must find the slope first. Then use the point slope formula
:
so I will use (0,17) and (1,23) to find the slope
:
23-17/1-0=6
:
so we have a slope=m=6
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now choose any point you would like and plug the values into the point slope formula. I choose the point (0,17)
:
y-17=6(x-0)
:
y-17=6x
:
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
The first thing to remember is that the t-chart gives you the coordinates for three ordered pairs representing points on the line, namely (0, 17), (1, 23), and (2, 29).
The numbers in this problem are actually simple enough that you can do this one pretty much in your head. So let's do it that way first, and then we'll do it the 'right' way just to prove it.
Notice that one of the given points has an x-coordinate of 0. That means that is the point where the line crosses the y-axis, also known as the y-intercept. The next thing to notice is that each time x increases by 1, y increases by 6 -- that tells us the slope is 6. So the equation must be:  .
Now let's do it the 'right' way and check on the reasonability of our answer. Given the ordered pairs that describe two points on a line, you can use the Two-Point form of the equation of a line to develop the equation.
The Two-Point form is:
(x - x_1)) where the two given points are: ) and ) .
It actually doesn't matter which of the three points you were given that you choose, so let's just take the first two:
) and ) .
(x - 0))
Do the arithmetic:
Add 17 to both sides:
which is the same result we obtained using the intuitive analysis.
Lastly, you should check to ensure that each of the given ordered pairs satisfy the equation:
 + 17) True
 + 17) True
 + 17) True
John
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