Proportional Relationships
What is two quantities have a proportional relationship if the ratio of quantity in the other is constant?
Meaning of Unit Rate
What is the rate in which the second quantity in the comparison is one unit?
How do you find the constant of proportionality on a table?
First, find the ratio by putting y/x (fraction) for each of the table entries. Then see if each of the fractions are equivalent fractions which means they are equal ratios. Meaning it has a constant of proportionality.
By looking at a graph, the two ways to know if it is proportional are:
1) The line is straight
2) If the line goes through the origin
Meaning of Reciprocal
What is one of two numbers whose product is 1?
What is in a proportional relationship, the constant unit rate, or K?
(How do you convert inches to feet?)
What is division by 12?
12:1
The number of teaspoons of sugar sed to decorate cookies is shown in the table on the slide.
Which color of sugar has a proportional relationship with the number of cookies decorated?
What is green sugar?
The graph on the slide shows the proportional relationship between the number of miles (y) and the number of hours (x).
1) The constant of proportionality is
2) What is an equation in terms of x and y that can be used to model the proportional relationship?
1) k=60
2) y=60x
Equation to find k if you know x and y
k=y/x
Fraction of y over x
The number of pages Jose reads over time is shown in the table on the slide.
1) What is Ella's rate of reading per hour?
2) Godwin reads at a rate of 65 pages per hour. What is the difference in the number of pages Ella and Godwin will read in 7 hours?
1) 35 pages per hour
2) 210 pages
At this rate, how many feet would the turtle travel in 1 hour? 1.5 inches in 1 second
What is 450 feet in 1 hour?
Morgan is making fresh-squeezed orange juice. There is a proportional relationship between the number of oranges, x, Morgan squeezes and the amount of juice in ounces, y, she makes.
What is the equation that represents the relationship between x and y?
The graph on the slide shows the proportional relationship between the number of miles (y) and the number of hours (x).
The point (2, 120) represents
What is in two hours the distance traveled is 120 miles?
Jack's town is building a pool based on a scale drawing that is 20 centimeters by 10 centimeters and uses the scale 1 cm : 250 cm. What is the area of the pool in square meters?
What is 1,250 meters2?
Miss Whited walks 20 feet in 6.5 seconds. What is Miss Whited's rate in miles per hour?
2.1 miles in 1 hour
Conversion of inches to miles
(what is the process of the conversion of inches to miles?)
1) Inches to Feet: by dividing by 12
2) Feet to Miles: by dividing by 5280
The amount of money Joel earns for walking dogs is shown in the table on the slide.
How much money in dollars does Joel earn for walking 15 dogs?
What is $78.75?
Properly graph the table on the graph paper on the board.
Then answer these questions:
1) Does the line go through the origin?
2) Does it have a proportional relationship?
1) No
2) No
Todd jogs 51 feet in 5.5 seconds. What is Todd's rate in miles per hour?
What is 6.3 miles per hour?