15. Five marks exercise problems IV

The data in the adjacent table depicts the length of a woman’s forehand and their corresponding height. Based on this data, a student finds a relationship between the height \((y)\) and the forehand length \((x)\) as \(y\) \(=\) \(ax\) \(+\) \(b\), where \(a\), \(b\) are constants.

 

Length '\(x\)' of forehand (in \(cm\))	Height '\(y\)' (in inches)
35	56
45	65
50	69.5
55	74

 

 

(i) Check if this relation is a function.

 

The given relation is not a functiona function 

 

(ii) Find \(a\) and \(b\).

 

\(a\) \(=\) 

 

\(b\) \(=\)  

 

(iii) Find the height of the woman whose forehand length is 40 \(cm\).

 

The height of the woman is  inches.

 

(iv) Find the length of the forehand of the woman if her height is 53.3 inches.

 

The length of the forehand \(=\) \(cms\)

 

[Note: Round off the answer to one decimal place.]