Presentation on theme: "Proportional Relationships"— Presentation transcript:
1Proportional Relationships Quantities have a constant ratio, or unit rateNonproportional relationships:Quantities do not have a constant ratio,or unit rate
2Example 1: The following chart shows how much money Layla earns babysitting. Is the amount of money she earns proportional to the number of hours that she spends babysitting?Hours (h)Money earned ($)15.50211.00316.50422.00Find the unit rate of money earned to hours worked for each pair of values.There is a proportional relationship between money earned and hours since all of the ratios have a unit rate of
3Plot points (x, y) from the table. Let’s graph this proportional relationship from Ex. 1 on an xy-plane.We typically put time (hours) on the x-axis, and the money earned ($) on the y-axis.yLayla’s Babysitting MoneyPlot points (x, y) from the table.22.00Hours (h)Money Earned ($)Point (x, y)15.50(1, 5.50)211.00(2, 11)316.50(3, 16.50)422.00(4, 22)16.50Money Earned ($)11.005.50x12345Hours workedThe graph of a proportional relationship:is a straight line, ANDit passes through the origin, or point (0,0).
4In words, Money earned = (money per hour)(number of hours) We can write an equation to represent the proportional relationship from Ex. 1.xyHours workedMoney Earned ($)15.5011.0016.5022.002345Layla’s Babysitting MoneyHours (h)Money Earned ($)15.50211.00316.50422.00In words, Money earned = (money per hour)(number of hours)As an equation, y = $5.50 x
5Example 2: Movie World charges a $6 monthly membership fee plus $1 per movie rental. Is the monthly cost proportional to the number of movies rented? Explain .Find the unit rate of the monthly cost to the number of rentals for each pair of values.Movies rented1234Monthly Cost ($)78910There is NOT a proportional relationship between monthly cost and number of movie rentals since all of the ratios between the two quantities are not equal.
6Let’s look at a graph this nonproportional relationship from Ex. 2. Movie rentals will be on the x-axis,and the monthly cost ($) will be on the y-axis.Monthly Cost of Movies from Movie Worldy16RentalsMonthlycost ($)Point (x, y)17(1, 7)28(2, 8)39(3, 9)410(4, 10)141210Cost ($)8642This graph shows a nonproportional relationship.Even though this graph is a straight line,it does not pass through the origin.x1234Number of movie rentals