Question

representing proportional relationships
emily can swim a distance of 350 meters in 7 minutes. write an equation to represent the relationship between x, the number of minutes and y, the distance swam.
$y=kx$
$k=\frac{y}{x}$
$k=\frac{350}{7}=50$
consider this:
when you divide 350 by 7, we know it is 50.
but, we can write that division as $\frac{350}{7}=\frac{y}{x}$
fill in the blank
for 350 meters, it took emily ____ minutes of swimming time.

Explanation:

Step1: Identify proportional constant

First, calculate the constant of proportionality $k$, which is the distance per minute.
$k = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{350}{7} = 50$

Step2: Form the proportional equation

Use the standard proportional relationship $y = kx$, where $x$ is time in minutes and $y$ is distance in meters. Substitute the value of $k$.
$y = 50x$

Step3: Fill in the blank

From the given context, the time taken for 350 meters is directly stated.
$7$

Answer:

The equation is $y = 50x$; the blank is filled with 7.