Constant of Proportionality In Words
Constant of Proportionality Equations
Tables and Graphs
Unit Rates/Slope
Comparing Proportional Relationships
100
Jude sends 45 E-mails in 15 minutes.
How many E-mails did he send per minute?
He sent 3 E-mails per minute.
100
Navelle earns $12 per hour. Write an equation that represents Navelle's earnings.
y = 12x
100
Is the rate of change for this table constant or variable? Explain.
The relationship is constant because if we divide each cost per number of tickets, we see the constant of proportionality is $1.50 per ticket.
100
Every 2.5 hours, a machine produces
2250 basketballs. What is the unit rate of this proportional relationship?
900 basketballs per hour
100
Which graph has the greatest slope? Explain
Line a
200
Lenasia earned $640 in a 40-hour work week.
What is Lenasia's hourly rate of pay?
Lenasia earns $16 per hour.
200
Gianna reads 27 pages in 9 minutes. At What rate does Gianna read?
Write an equation for this relationship.
Gianna reads 3 pages per minute.
y = 3x
200
Is the rate of change for this table constant or variable? Explain.
The rate of change is variable because when we divide the sales of ice cream by each Temperature, we do not get a constant value.
200
What is the slope formula?
m = y2 - y1
x2 - x1
200
Which relationship has the greater slope? Explain.
y = 7x
or
?
y = 7x ; slope (m) = 7
The graph is y = 6x ; slope (m) = 6
7>6
300
A helicopter propeller spins 2400 revolutions in 4 minutes. What is the constant of proportionality (k), in revolutions per minute?
The constant of proportionality is k = 600 RPM.
300
Maxine works at law office. the equation y = 135x represents her earnings.Determine how much money she makes if she works 40 hours.
Maxine earns $5,400 in 40 hours.
300
A graph represents a proportional relationship if:
1.
2.
1. It is a straight line
2. It passes through the origin
300
What is a the slope of a line that passes through the origin and goes through point (3, 9)?
m = 3
300
Which has the greater slope? Explain.
The equation y = 1.5x or the table below:
The equation has the greater slope because 1.5 is greater than 1.25.
400
Jeff earned $400 working a 40-hour work week.
Find Jeff's hourly wage and use it to predict how much he will make if he works for 47 hours.
Jeff makes $10 per hour and would make $470 IN 47 hours.
400
The equation y = 55x represents the rate of the Long Island highway speed limit, in miles per hour. Let x represent the number of hours driven and y represent the total miles driven.
How long was Francis driving if he drove 247. 5 miles at the speed limit.
Francis drove for 4.5 hours.
400
What is the slope of this graph?
m = 1/6
400
Find the slope of a line that passes through the points (2, 4) and (4, 12).
m = 4
400
Which has the lesser slope? Explain.
The graph?
or the word problem: Jesse completed 10 laps in 18 minutes. How many laps did he run in 1 minute?
The graph is 2/3 of a lap per minute, or 6/9 of a lap per minute.
The Word problem is 5/9 of a lap per minute. Since 6/9 > 5/9, then 2/3 is greater than 5/9 so the word problem gives the lesser slope.
500
Janine sells 16 apples for $8.00. What is the unit price for each apple?
How much would she earn if she sold 64 apples?
The unit price is $0.50 per apple.
Janine would earn $24 for selling 64 apples.
500
If Jackson ate hamburgers at a rate of 3.5 hamburgers per minute and Jacen ate hamburgers at a rate of 4.7 hamburgers per minute, write an equation that could represent how many more hamburgers Jacen can eat more than Jackson.
y = 1.2x
500
What is the slope of this line?
The slope is undefined.
500
Which line has a slope of 2?
Line m
500
Which relationship has the greater slope? The table or the graph. How do you know?
Well A Pumps water at a faster rate at 2.75 barrels per hour. Where Barrel B pumps water at 2.5 barrels per hour.