Question

Decide whether or not each equation represents a proportional relationship. A.The remaining length (L) of 120-inch rope after x inches have been cut off: 120−x=L b.The total cost (t) after 8% sales tax is added to an item's price (p): 1.08p=t c.The number of marbles each sister gets (x) when m marbles are shared equally among four sisters: x=m4 d.The volume (V) of a rectangular prism whose height is 12 cm and base is a square with side lengths s cm: V=12s2 Problem 3

Answer 1

Answer and Step-by-step explanation: An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same. For example, in general:

Equation: y = mx

$\frac{y}{x}$ = m

m is a constant value, which means is the same.

A. Equation: 120 - x = L

Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.

B. Equation: 1.08p = t

Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.

$\frac{t}{p}=1.08$

C. Equation: $x=\frac{m}{4}$

This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:

$\frac{m}{x}=4$

D. Equation: $V=12s^{2}$

This equation is NOT proportional because side length is squared, so it is not constant linearly.