Question

A yogurt machine makes

gallon of yogurt
every minute. The total amount y that the
machine makes in x minutes is given by
the equation y
]×. Determine whether the
relationship between x and y is linear and, if
so, if it is proportional,

Answer 1

Explanation:

the relationship between x and y is defined by a constant factor.

you can "go" from x to y and from y to x consistently and without any interruptions by applying that constant factor.

that makes it a linear relationship (a line on a chart, hence the name).

proportional relationships are relationships between two variables where their ratios are equivalent. another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

so, yes, it is proportional.

and the table is then

x y

0 0

3 3×2/3 = 2

6 6×2/3 = 4

9 9×2/3 = 6