<p>"f is a linear function; the following are some values:</p>
<p>x= 0; f(x)= a</p>
<p>x= 1; f(x)= 24</p>
<p>x= 2; f(x)= b</p>
<p>what is the value of a + b?"</p>
<p>a) 24
b) 36
c) 48
d) 72
e) It cannot be determined from the information given</p>
<p>cannot be determined without the slope of the line. Think about it. The line could rotate around that point (1,24).</p>
<p>I put (e) too, but it was wrong..the real answer is 48 o_0</p>
<p>i think its cuz when ur given x=0, x=1, x=2 the x=1 should be the midpoint if its linear function, therefore if midpoint is 24, b should be 48 and a 0, not sure just assuming, i could try to test it out and stuff but i'm to lazy right now</p>
<p>it doesnt matter what the slope is because you know that the function is linear, and point a is going to be just as much above/below point (1,24) as point b is going to be above/below the same point...so the sum is the middle...sorta like -7 +7 = 0, the middle.</p>
<p>think about it; if the function were f(x) = 24x, or if it were f(x) = x+23, or whatever the answer would still come out to be 48.</p>
<p>It is linear, so the difference of a and 24 will equal the difference of 24 and b.
|24 - a| = |24 - b|</p>
<p>Let's say a = 24 - k
Then b = 24 + k</p>
<p>Add them together.</p>
<p>? = a + b
? = (24 - k) + (24 + k)
? = 24 - k + 24 + k
? = 24 + 24 + k - k
? = 48</p>
<p>You could have just picked numbers by making up any slope.</p>
<p>Slope of m --> a + b
Slope of 1 --> 23 + 25
Slope of 7 --> 17 + 31
Slope of -10 --> 34 + 14</p>
<p>They all equal 48.</p>