Vocabulary
Unit Rate
Proportional or Nah
Slope
Y-intercept
100
A rate where the second term (denominator) is 1 unit. It's often expressed as a quantity per one unit.
Unit Rate
100
If a runner travels 15 miles in 3 hours, what is their average speed in miles per hour?
5 miles per hour
100
Look at the graph below. Does the line represent a proportional relationship? Explain your answer in one sentence.
Yes, the graph represents a proportional relationship because the line is straight and passes through the origin (0, 0), and has a constant rate of change.
100
What letter in this equation represents the slope?
y = mx + b
m
100
In the equation y = 7x - 12, what is the y-intercept?
-12
200
The point where the graph of a line crosses the y-axis. In the linear equation y = mx + b, it is represented by the b, and the point is (0, b).
Y-intercept
200
Which store offers the better unit price for juice?
H-E-B: 4 liters for $3.80
Walmart: 2.5 liters for $2.50
STORE A
H-E-B: = $0.95 per liter
Walmart: = $1.00 per liter
Since $0.95<$1.00, H-E-B offers the better unit price.
200
Tickets (x) Cost (y)
1 $9
3 $27
5 $45
yes, the constant of proportionality is 9 each time.
200
A line passes through the points (4, 1) and (-2, 13).What is the slope of the line?
Slope = -2
200
What is the y-intercept on the graph below?
(0,5) 5
300
The measure of the steepness and direction of a line. In the linear equation y = mx + b it is represented by m.
Slope
300
A bakery uses 3 cups of flour to make 18 cookies. If they want to make 96 cookies for a special event, how many cups of flour will they need?
Step 1: Unit Rate = cups of flour per cookie
1/6 cup per cookie
Step 2: Use unit rate and multiply by 96 cookies
= 16 cups of flour.
300
yes because it goes through origin, its a straight line and changes at a constant rate
300
The table shows the number of words typed over time. What is the rate of change in words per minute?
Minutes (x) Words Typed (y)
2 80
5 200
8 320
40 words per minute
300
The table shows the temperature of a frozen pizza over time as it bakes. What is the y-intercept, and what does it represent in this context?
Time in minutes (x) Temperature (y)
0 40
5 120
10 200
y-intercept: 40
Context: It represents the starting temperature of the pizza (40) right before it was put into the oven (at Time 0 minutes).
400
A relationship between two quantities where the ratio of one quantity (y) to the other quantity (x) is constant.
Proportional Relationship
400
Two families are arguing about who is getting better gas mileage on their summer road trips.
The Smith Family drove 480 miles and used 80 gallons of gas.
The Jones Family drove 390 miles and used 65 gallons of gas.
Which family's car got better gas mileage (more miles per gallon, or MPG)?
They both got the exact same gas mileage.
6 MPH
400
Which equation represents a proportional relationship and why?
A) y = 5x + 3
B) y = 1/2x
C) y = x2
A proportional relationship must be in the form y = kx, where k is the constant of proportionality and the y-intercept is 0 (it passes through the origin).
A is not proportional because of the +3.
C is not proportional because x is squared.
B is proportional with a constant of proportionality of k = 1/2
400
What is the relationship between y and x? write an equation to represent the relationship.
Slope = -3/2
Y- intercept = (0,3)
Equation: y= -3/2x + 3
400
A carnival charges a flat entry fee and then a price per ride. The table below shows the total cost based on the number of rides purchased.
Rides (x) Total Cost (y)
0 $12.50
2 $17.50
4 $22.50
y-intercept: $12.50
Slope: 2.50
y = 2.50x + 12.50
Context: It represents the flat entry fee of $12.50 that you must pay even if you go on 0 rides.
500
The variable in a relationship that is chosen or controlled and does not depend on the other variable. It is usually plotted on the x-axis.
Independent Variable