Podcast Beta
Questions and Answers
What is the slope when given the points (0, -2) and (3, 4)?
Using the ski rental package table, what is the cost per additional person?
What is the slope derived from the time and distance table?
Calculate the slope between the points (10, -1) and (-8, 6).
Signup and view all the answers
From the ski rental package table, what is the total cost for 4 people?
Signup and view all the answers
Study Notes
Calculating Slope from Points and Tables
- Slope formula: (m = \frac{y_2 - y_1}{x_2 - x_1}) calculates the rate of change between two points.
- For points (0, -2) and (3, 4):
- (m = \frac{4 - (-2)}{3 - 0} = \frac{6}{3} = 2), indicating a positive slope.
- Selecting points from a table follows the same process; the slope remains consistent regardless of the source (points or tables).
Slope Example from Given Points
- To find the slope for points (10, -1) and (-8, 6):
- Calculate using the formula:
- (m = \frac{6 - (-1)}{-8 - 10} = \frac{7}{-18} = -\frac{1}{6}).
Cost per Person in a Rental Package
- A table shows costs for a ski rental package:
- Cost increases consistently at $40 per additional person.
- At 4 people, the total cost is $160, equating to $40 per person.
- Slope: (m = \frac{1}{40}) dollars per room, with each person's cost being $40.
Distance Travelled Over Time
- Another table outlines distance driven over specified times:
- Incrementally, distance rises by 102 miles every 2 hours.
- This translates to a rate of 51 miles per hour, derived from (m = \frac{102}{2} = 51).
Key Definitions
- Slope: Represents the steepness or incline of a line, indicating how much y changes for a unit change in x.
- Linear relationship: Demonstrated through consistent rates of change in data tables.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz explores how to calculate the slope of a line given two points or a set of values in a table. You'll learn to use the slope formula effectively and apply it in different scenarios. Test your understanding with various question types to solidify your knowledge.
