SOLUTION: What are the values of a and b that complete the table representing the linear function. x k(x) -3 -5.5 0 b 3 9.5 a

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Question 957582: What are the values of a and b that complete the table representing the linear function.
x k(x)
-3 -5.5
0 b
3 9.5
a 17
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x| k%28x%29
-3+|-5.5
0|+b
3+|+9.5
a+|1
k%28x%29=mx%2Bc ....where m is a slope and c y-intercept
-3|-5.5
-5.5=m%2A%28-3%29%2Bc
-5.5=-3m%2Bc
c=3m-5.5.............1

3+|+9.5
9.5=m%2A3%2Bc
c=9.5-3m.............2
from 1 and 2, we have
3m-5.5=9.5-3m.........solve for m
3m%2B3m=9.5%2B5.5
6m=15
m=15%2F6
m=5%2F2
find c
c=9.5-3m.............2
c=9.5-3%285%2F2%29
c=9.5-7.5
c=2
so, your equation is: k%28x%29=%285%2F2%29x%2B2

x| k%28x%29
-3+|-5.5
0|+2 =>k%280%29=%285%2F2%290%2B2=>b=2
3+|+9.5
-2%2F5|1=>1=%285%2F2%29a%2B2=>%285%2F2%29a=1-2=>%285%2F2%29a=-1=>a=-1%2F%285%2F2%29=>a=-2%2F5