Question

50 POINTS

This table represents a proportional relationship.

What is the constant of proportionality for this proportional relationship?
• 1/10
• 8/9
• 10

Answer 1

`\huge \sf༆ Answer ༄`

According to the question ;

`{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y \propto x`

Now, let's add a constant of proportionality to replace proportionality sign with equal to :

`{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = kx`

[ where, k is proportionality constant ]

plug the value of x and y from any ordered pair in the table , for example :
`\sf((1)/(5) , 2)`

`{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:2 = k * (1)/(5)`

`{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:k = 2 * 5`

`{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:k = 10`

Therefore, value of proportionality constant (k) is

`\overbrace{  \underbrace{\underline{ \boxed{ \sf 10 }}}}`