Question

a touchdown is worth 6 points. Additionally you score an extra point if you kick a field goal. is the total number of points scored proportional to the number of touchdowns?

Answer 1

No; since there is the added possibility of field goals, the number of points is not proportional to touchdowns. If only touchdowns were possible, then yes, it would be proportional.

Answer 2

Number of points scored in a touchdown =6 points

If you kick a field goal then number of points=1

Suppose , Number of touchdown = x

Then total points scored in touchdown =6x

And number of field goal =y

Then number of points in field goal = y

Total number of points which includes touchdown and field goal =6x+y

→Number of points scored in touch down can be proportional to Total number of points which includes touchdown and field goal , if number of field goals will be equal to multiple of 6,that is y=6n, where n=0,1,2,3,.....

For proportional relationship

→6x ∝ 6x+y

→6x ∝ 6x+6n

→6x ∝ 6×(x+n)----Proportional relationship

→If y is not multiple of 6, then the two, total number of points scored will not be proportional to the number of touchdowns.

→6x and 6x+y will not be proportional.