Question

describe methods you can use to show a proportional relationship between two variables, x and y. for each method, explain how you can find the unit rate and the slope.

Answer 1

Table of Values: The ratio of (Y) to (X) gives the unit rate and slope.

Equation: If the equation can be written as y=mx, then m is the unit rate and the slope.

Graph: When the line passes through the origin, the slope of the graph gives the unit rate and the slope.

Explanation:

you can just copy everything here, its in the teacher's book

Answer 2

If the ratio of x/y or x/y is always the same constant, then a and y are directly proportional and the constant is called the constant of proportionality.

If the product of xy is always the same constant, then a and y are inversely proportional and the constant is called the constant of proportionality.

unit rates --- are like any rate found by dividing --- like speed --- miles per hour unit means 1 and this is miles traveled in one hour (at constant speed) --- so you just divide --- traveling 100 miles in 2 hours = 50 miles in 1 hour --- 50 miles per hour --- miles/hour <<< that is a unit rate

slope is a rate of change --- on an x-y coordinate axis graph the slope is the rate of change of y compared to a change in x --- this is not necessarily a unit rate ... slope of 2/3 means a change of 2 for y will create a change of 3 for x (not a change of 1, so it is not a unit rate)