SOLUTION: the equation of function G is y=2x+6. The table shows some of the points of function H. x|y 2|2 4|5 6|8 what is the difference in the y-intercepts of the two fun

Algebra ->  Functions -> SOLUTION: the equation of function G is y=2x+6. The table shows some of the points of function H. x|y 2|2 4|5 6|8 what is the difference in the y-intercepts of the two fun      Log On


   

Question 1151343: the equation of function G is y=2x+6. The table shows some of the points of function H.
x|y
2|2
4|5
6|8
what is the difference in the y-intercepts of the two functions?
A. 6
B. 7
C. 8
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
H(x) has points
( 2,2 )
( 4,5 )
( 6,8 )
-----------
+y+=+m%2Ax+%2B+b+
(2,2)
+2+=+m%2A2+%2B+b+
+2m+%2B+b+=+2+
----------------------
(4,5)
+5+=+m%2A4+%2B+b+
+4m+%2B+b+=+5+
----------------------
Subtracting:
+4m+%2B+b+=+5+
+-2m+-+b+=+-2+
-----------------------
+2m+=+3+
+m+=+3%2F2+
and
+2m+%2B+b+=+2+
+2%2A%283%2F2%29+%2B+b+=+2+
+b+=+-1+
------------------------
The equation is:
+y+=+%283%2F2%29%2Ax++-+1+
check:
(6,8)
+8+=+%283%2F2%29%2A6+-+1+
+8+=+9+-+1+
+8+=+8+
OK
--------------------
The y-intercepts are +6+ and +-1+
+6+-%28-1%29+=+7+
Answer is B. 7

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Since the problem doesn't say that function H is linear, the problem really can't be answered.

However, since the given points of function H SEEM TO INDICATE that the function is linear, we can go ahead and work the problem.

(2) Having assumed that H is a linear function, there is no need to go through the formal mathematics shown by the other tutor (although that might be good for learning purposes). It is very easy to find the y-intercept of function H informally.

H(4)=5; H(2)=2.
Since the function is linear, that means decreasing x by 2 decreases y by 3.
That means H(0) (the y-intercept, which we want) is 3 less than H(2): 2-3 = -1.

So the y-intercepts of the two functions are 6 and -1; the difference is 7.