Question

Describe methods you can use to show a proportional relationship between two variables, x and y. For each method, complete the explanation of how you can find the unit rate and the slope.

Answer 1

To show a proportional relationship between two variables x and y, you can use the methods of directly proportional, graphing, and calculating the slope.

Step-by-step explanation:

There are several methods you can use to show a proportional relationship between two variables, x and y:

1. Directly Proportional: Two values or constants are directly proportional when a change in one leads to the same change in the other. This is represented by the equation y = kx, where k is the proportionality constant. The unit rate or slope in this case is the value of k.
2. Graphing: Plot the variables on a graph and if they form a straight line passing through the origin (0,0), then there is a proportional relationship. The slope of the line represents the unit rate.
3. Calculating the Slope: If you have a set of data points, you can find the slope by using the formula m = (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are any two points on the line. The slope represents the unit rate.