Posted - 05/07/2007 : 11:56:24
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?
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
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