four students were discussing how to find the unit rate for a proportional relationship. which method is…

four students were discussing how to find the unit rate for a proportional relationship. which method is valid?\n“look at the graph of the relationship. find the y - value of the point that corresponds to x = 1. that value is the unit rate.”\n“look at the graph of the relationship. count the number of units up and the number of units to the right one must move to arrive at the next point on the graph. write these two numbers as a fraction.”\n“look at the graph of the relationship. find the x - value of the point that corresponds to y = 2. that value is the unit rate.”\n“look at the graph of the relationship. find two points which have y - values that are one unit apart. the unit rate is the difference in the corresponding x - values.”

four students were discussing how to find the unit rate for a proportional relationship. which method is valid?\n“look at the graph of the relationship. find the y - value of the point that corresponds to x = 1. that value is the unit rate.”\n“look at the graph of the relationship. count the number of units up and the number of units to the right one must move to arrive at the next point on the graph. write these two numbers as a fraction.”\n“look at the graph of the relationship. find the x - value of the point that corresponds to y = 2. that value is the unit rate.”\n“look at the graph of the relationship. find two points which have y - values that are one unit apart. the unit rate is the difference in the corresponding x - values.”

Answer

Explanation:

Step1: Recall unit - rate concept

For a proportional relationship $y = kx$, the unit rate $k$ is the value of $y$ when $x = 1$.

Step2: Analyze each option

  • Option 1: Looking at the $y$-value when $x = 1$ gives the unit rate for a proportional relationship. This is correct.
  • Option 2: Counting units up and right and writing as a fraction gives the slope (which is the unit - rate for a proportional relationship), but the description is not the standard way to find the unit rate.
  • Option 3: Finding the $x$-value when $y = 2$ is not related to finding the unit rate. The unit rate is the value of $y$ per 1 unit of $x$.
  • Option 4: Finding the difference in $x$-values for $y$-values one unit apart is not the correct way to find the unit rate.

Answer:

"Look at the graph of the relationship. Find the $y$-value of the point that corresponds to $x = 1$. That value is the unit rate."