Proportional Relationships

Constant of Proportionality

100

What letter represents the constant of proportionality?

k

200

How do we find the constant of proportionality?

k=y/x

300

Identify the constant of proportionality in this equation y=2/3x

k=2/3

400

Brandon's phone bill costs $30 each month. What is the unit rate or constant of proportionality?

$30 

or

k=30

500

At Kroger, 6 pounds of chicken thighs costs $52.50. What is the unit rate or constant of proportionality?

k=8.75

or 

$8.75 per pound of chicken

Slope

100

What letter represents slope?

m

200

Slope is the same as...

Constant 

or

Unit rate

300

A line which is decreasing has a _________ slope.

Negative

400

How do you find slope when given two points or ordered pairs?

m= y₂-y_1/x₂-x₁

500

Find the slope of the line containing the points (2, 5) and (7, 9)

m=4/5

Writing Equations

100

Write an equation for a line with a constant of 1/4 and a y-intercept of 0

y=1/4x

200

Netflix charges a sign-up fee of $20 and it costs $12 a month to keep your subscription. Write an equation that represents this situation.

y=12x+20

300

Write the equation of the line whose slope is 6 and y-intercept is -7.

y=6x-7

400

I read 20 pages of my book each night. Write an equation that represents this situation where y is total number of pages read, and x is number of nights.

y=20x

500

Katie's phone plan costs $200 to start. There is a $50 monthly charge for service. What is the total cost for x months?

y=50x+200

Comparing Rates

100

Dunkin charges $2.75 for a refresher. Starbucks charges $3.50 for a refresher. Who charges more? How much more?

Starbucks charges $0.75 more for a refresher.

200

The equation y=4x represents the cost per Big Mac at McDonalds, where y represents total cost, and x represents number of Big Macs purchased. Whoppers at Burger King cost $2.50 each. Who charges more for a burger? How much more?

McDonalds charges $1.50 more for a burger than Burger King.

300

Ryan runs 3 miles in 27 minutes. The equation y=11x represents Rickie's rate where y represents total distance, and x represents number of miles. Who runs at a faster rate? How much faster?

Ryan runs at a faster rate, 2 minutes faster than Rickie.

400

Two friends, Quentin and Olivia, took summer jobs. The equation y=21.50x represents Quentin's earnings in dollars and cents, y, for working x hours. Olivia earned $457.20 in 18 hours. Who makes more money per hour? How much more?

Olivia makes $3.90 more than Quentin per hour.

500

Hudson was comparing the price of orange juice at two stores. The equation y=0.57x represents what Hudson would pay in dollars and cents, y, for x bottles of orange juice at store A. Hudson can buy 17 bottles of orange juice at Store B for a total cost of $13.26. How much more is a bottle of orange juice at Store B than at Store A?

1 bottle of orange juice costs $0.21 more at Store B than at Store A.