the data in the adjacent table depicts the length of a woman forehand and her corresponding height. based on this data, a student find a relationship between the height y and the forehand length x as y=ax+b, where a and b are constant
i) check if this relation is a function
ii) find a and b
Answers
Answer:
This relationship is not a function
its is a function if 65.5 is changed to 65.45
a = 0.9
b = 24.5
Step-by-step explanation:
Length'x' of forehand (in cm )45.5,35 ,45,50,55
height 'y' (in inches) 65.5,56,65,69.5,74
y = ax + b
65.5 = a45.5 + b
56 = a35 + b
65 = a45 + b
69.5 = a50 + b
74 = a55 + b
Using 65.5 = a45.5 + b & 65 = a45 + b
=> 0.5 = a0.5
=> a = 1
b = 20
y = x + 20
65.5 = 45.5 + 20 TRUE
56 = 35 + 20 FALSE
65 = 45 + 20 TRUE
69.5 = 50 + 20 FALSE
74 = 55 + 20 FALSE
This relationship is not a function
if we make slight change in data
Length'x' of forehand (in cm )45.5,35 ,45,50,55
height 'y' (in inches) 65.45,56,65,69.5,74
then 0.45 = 0.5a
=> a = 0.9
65 = 0.9 *45 + b
=> b = 24.5
y = 0.9x + 24.5
65.45 = 0.9*45.5 + 24.5 = 65.45 TRUE
56 = 0.9*35 + 24.5 = 56 TRUE
65 = 0.9*45 + 24.5 =65 TRUE
69.5 = 0.9*50 + 24.5 = 69.5 TRUE
74 = 0.9*55 + 24.5 = 74 TRUE
Here its is a function
a = 0.9
b = 24.5
Answer:
Why didn't change both the numbers in cm or in inches? Height in inches and length in cm using which we should do the sum?