<p>Question One:</p>
<p>Table:
x | f(x)
0 "b"
1 24
2 "a"</p>
<p>The table above represents linear function "f", what is the value of a+b...
a.24
b.36
c.48
d.72
e.Cannot be determined from info given</p>
<p>I put E down because clearly there are an infinite number of lines passing through a single point on a plane and you need 2 coordinates to get a concrete line. But the answer is C, I know it is the only possible one of the answer choices if you guess and check, but I still feel that a better answer is E though, what do you think? PS. Is Cannot be determined ever an answer??</p>
<p>You are right that there are an ifinite # of lines that pass thru (1,24). But try making up a couple of examples and you will discover that f(0) and f(2) always add up to 48. Draw the diagrams and I bet you’ll see why it works: if the graphs are linear, since 0 and 2 are both one away from 1, f(0) and f(2) will differ from f(1) by the same amount…one higher and one lower (or all three the same).</p>
<p>Because we know the function is linear, the slope is constant. And we are given 3 points : (0,b) (1,24) (2,a). Thus, the slope between the first 2 points must be equal to the slope between the second 2 points .so we have (24-b)/(1-0)= (24-a)/(1-2) -> (24-b)=-24+a -> 48 = a+b, as desired. C.</p>
<p>Quicker ways:</p>
<p>Method 1: A linear function has a constant slope. This means that equal jumps in x yield equal jumps in y. Note that the jumps in x ARE equal (each jump is 1). Therefore the jumps in y are also equal. So just choose any values for a and b that give equal jumps. For example, we can let b=0 and a=48. Then a+b=48.</p>
<p>Another example is a=23, b=25. Again a+b=48. So a good guess would be C.</p>
<p>Method 2: Since the jumps in x are equal, so must be the jumps in y. Thus 24 must be the average of a and b. So the sum of a and b is 48.</p>
<p>24-a / 1-2 = 24-b / 1-0…why? Because it’s the three points are linear, so their slopes are equal
Therefore;
-24+b = 24-a
Therefore;
a+b = 24+24 = 48</p>