Slope
Which line has the largest slope?
Line A
1) What is another word for slope?
2) How does slope move?
1) Rate of Change
2) Rise/Run
What is the slope and what is the y-intercept in the equation:
y = -5x - 12
Slope: -5
y-intercept: -12
Graph the equation y = 3/2x - 8
Positive Line starting at -8, moving up 3 and right 2.
Katie is comparing costs of bananas at two different grocery stores. Store A is represented by the table. Store B is represented by the equation.
What is Store A's rate?
What is Store B's rate?
A: $1.25 per pound
B: $1.75 per pound
If student B is running at rate of 580 feet per minute, their equation would be y=580x, where y represents the number of miles and x represents the number of minutes.
Write an equation that could represent student A and an equation that could represent student C.
Student A: y = (>580)x
Student C: y = (<580)x
What is the slope of the line?
8/3
What does y-intercept mean? How does it help us when graphing?
It is where it crosses the y-axis. We start on the y-axis at the y-intercept.
Write an equation of the line.
y = -2/5x
Polly and Olivia are saving money for an upcoming trip. Polly’s savings are represented by a table. Olivia’s savings are represented by a graph.
What is Polly’s rate?
What is Olivia’s rate?
Who saves more? How much more?
Polly: $16.50 per month
Olivia: $12 per month
Polly saves more. She saves $4.50 more per month.
Anthony is looking into theme parks for his family vacation. The graph shows the cost of a specific theme park after buying admission and a certain number of tickets.
What is the slope of the line and what does it mean in this context?
The slope is 2. It means $2 per ticket.
What is the slope of the line?
-1/2
Anthony is looking into theme parks for his family vacation. The graph shows the cost of a specific theme park after buying admission and a certain number of tickets.
What is the y-intercept of the line and what does it mean in this context?
The y-intercept is 20. It means it costs $20 to get in the theme park.
Using the four types of slope, label each graph:
Positive, Negative, Zero, Undefined
Positive - Increase
Negative - Decrease
Zero - Horizontal
Undefined - Vertical
Two families are traveling to Florida. The Oscar Family’s trip is represented by the equation. The Smith Family’s trip is represented by the graph.
What is the Oscar Family’s rate?
What is the Smith Family’s rate?
Which family is traveling faster? How much faster?
Oscar Family: 60 miles per hour
Smith Family: 65 miles per hour
The Smith Family is traveling 5 miles per hour faster.
Find the slope of the line that goes through the points (-8, 25) and (12, -15). Make sure the slope is in simplest form.
-2
Two teams, A and B, are walking in the town’s marathon. Team A walked at a constant speed of 12 miles per hour.
1) Looking at the graph, is Team B faster or slower than Team A?
2) Write an equation that could represent Team B’s rate.
Team B is faster.
y = (>12)x
To paint a house, a painting company charges a flat rate of $500 for supplies plus $50 for each hour of labor.
1) Write an equation of the line.
2) What is the y-intercept of the line and what does it mean in this context?
y = 50x + 500
The y-intercept is 500. The initial value to paint the house is $500.
Write an equation of the line.
y = 1/3x - 5
Two amusement parks charge a constant rate for tickets. Amusing Rides is represented by the table. Lots of Laughs is represented by the graph.
What is Amusing Ride’s rate?
What is Lots of Laugh’s rate?
Which amusement park is cheaper? How much cheaper?
Amusing Rides: $1.50 per ticket
Lots of Laughs: $2.50 per ticket
Amusing Rides is $1 cheaper per ticket.
Look at the graph of the proportional relationship between the amount of fish (in grams) and the number of calories consumed.
What is the slope of the line and what does it mean in this context?
Slope is 3/2. 1.5 calories per fish.
The graph shows the amount of gas in Brad’s tank as he drives a certain number of miles.
What is the slope of the line and what does it mean in this context?
Slope is -1/10. Lose 0.10 gallon per mile.
Customers at a gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the scenario.
What is the y-intercept of the line and what does it mean in this context?
The y-intercept is 60. Customers pay $60 to join the gym.
Graph the equation y = -x + 3
Negative Line. Start at 3 on the y-axis, move down 1 right 1.
Paul is comparing apple prices at two different apple orchards. Apple Farm is represented by the equation. Awesome Apples is represented by the graph.
What is Apple Farm’s rate?
What is Awesome Apple’s rate?
Which apple orchard is cheaper? How much cheaper?
Awesome Apples: $4 per pound
Awesome Apples is cheaper by $0.50 per pound.