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Haven
Senior Member

USA
28 Posts

Posted - 05/07/2007 :  11:06:05  Show Profile  Reply with Quote
The problem: The table below shows some values for the function f. If f is a linear function, what is the value of a + b?

x f(x)

0 a
1 24
2 b

The answers:

a) 24
b) 36
c) 48
d) 72
e) It can not be determined from the information given

The answer given was "c" but there was no explaination given. How was this answer determined.

Any help would be greatly appreciated
Haven
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Mrspi
Advanced Member

USA
998 Posts

Posted - 05/07/2007 :  11:56:24  Show Profile  Reply with Quote
quote:
Originally posted by Haven

The problem: The table below shows some values for the function f. If f is a linear function, what is the value of a + b?

x f(x)

0 a
1 24
2 b

The answers:

a) 24
b) 36
c) 48
d) 72
e) It can not be determined from the information given

The answer given was "c" but there was no explaination given. How was this answer determined.

Any help would be greatly appreciated
Haven



If the function is linear then the ratio of the change in y to the change in x is the same for any pair of points. This ratio represents the slope of the line.

We are given these points: (0, a), (1, 24) and (2, b)

For the first two points, this ratio (the slope) is (24 - a) / (1 - 0), or (24 - a) / 1, or just 24 - a.

For the last two points, the slope is (b - 24) / (2 - 1), or (b - 24) / 1, or just b - 24.

The slope is the same for any two points on a given line. So,

24 - a = b - 24

Add "a" and 24 to both sides:
24 - a + a + 24 = b - 24 + a + 24
48 = b + a

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Haven
Senior Member

USA
28 Posts

Posted - 05/07/2007 :  12:38:04  Show Profile  Reply with Quote
Thank You very much, Mrspi
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