SOLUTION: I am trying to determine the value of "x" from the following problem: "This linear equation; What function of f(x) when x = 0"? (x) f(x) 2

Question 1143048: I am trying to determine the value of "x" from the following problem:
"This linear equation; What function of f(x) when x = 0"?
(x) f(x)
2 30
9 16
x 10
I tried drawing a graph, but it was not linear because I thought x was 3, since it is 1/2 the difference of 16 and 10. (The pattern is the same for the previous numbers).
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You are given 2 actual points, which is enough
to give you the slope
( 2,30 )
( 9,16 )
The slope is [ change in y ] / [ change in x ]

--------------------
Now you can use point ( x, 10 ) and either of the
given points to find

---------------------
Find the equation

Use the point ( 12, 10 ) or one of the other 2 points

The equation is:

-------------------------
check:
does it go through ( 9, 16 ) ?

OK
You can check ( 2, 30 )

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Thank you for telling us something about how you tried to solve the problem. It helps immensely to let us know where your thinking went wrong and how to fix it.

You say you thought x should be 3 because it is half the difference between 16 and 10. That indicates that you recognized from the two points (2,30) and (9,16) that the change in x is half the change in y (30-16 = 14; 9-2 = 7; 7 is half of 14).

What you did wrong was to think that 3 was the VALUE of x, whereas in fact it is the DIFFERENCE in the x values when the y value changes from 16 to 10.

(1) (2,30) to (9,16) tells us that y decreases by 14 when x increases by 7; so the change in x is half the change in y.

(2) Then, given (9,16) and (x,10), we see that the change in y is 6, so the change in x has to be half of 6, which is 3.

(3) Finally, seeing that y decreases when x increases, and seeing that y has decreased from 16 to 10, we see that x had to increase by 3.... So the new value of x is 3 more than 9, which is 12.
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