Question

A table contains the ordered pairs (3, 42.25) and (5, 50.75). If the relationship in the table is linear, explain how to find the initial value.

Answer 1

you can solve this in several ways. When the relationship is linear, it means the pairs are on a straight line. Therefore any other pair should be located on that line and the problem is to find the equation associated with the line. The slope of the line can be calculated as below:

Answer 2

\[\frac{ y2-y1 }{ x2-x1 }\]

Answer 3

which is: m=slope=(50.75-42.25)/(5-3) therefore the line can be written in this form: y-y1=m(x-x1)

Answer 4

the line eq is: \[y-(50.75)=4.25(x-5)\] and finally it is: \[y=4.25x+29.5\] using this equation you can find all other pairs

Answer 5

the second approach is to find the unknown coefficient within these two linear equations: \[3a+b=42.25\] and \[5a+b=50.75\] which the answer is a=4.25 and b= 29.5. and therefore all the associated pairs on the table satisfy this relation:\[y=4.25x+29.5\]

Answer 6

therefore if we consider x=0 for the initial value it gives y=4.25*0+29.5=29.5