Podcast
Questions and Answers
What is the slope of the line segment with endpoints A (2, 1) and B (5, 3)?
What is the slope of the line segment with endpoints A (2, 1) and B (5, 3)?
- 1/2
- 1
- 3/2
- 2/3 (correct)
Given the points C (−3, 4) and D (−1, −2), what is the slope of the line segment connecting them?
Given the points C (−3, 4) and D (−1, −2), what is the slope of the line segment connecting them?
- 2
- −3 (correct)
- 3
- 1
If the line segment joining the points (6, y) and (9, 10) has a slope of −2, what is the value of y?
If the line segment joining the points (6, y) and (9, 10) has a slope of −2, what is the value of y?
- 4
- 6
- 8 (correct)
- 2
Which pair of line segments are parallel based on the given slopes: mAB = 2, mJK = 2, mMN = −2?
Which pair of line segments are parallel based on the given slopes: mAB = 2, mJK = 2, mMN = −2?
What is the value of x so that the line segments connecting points R (x, 5) and S (6, 3) is parallel to the segment connecting T (−1, −6) and U (3, 2)?
What is the value of x so that the line segments connecting points R (x, 5) and S (6, 3) is parallel to the segment connecting T (−1, −6) and U (3, 2)?
What does the x-intercept of a graph represent?
What does the x-intercept of a graph represent?
Which of the following characteristics is true for functions?
Which of the following characteristics is true for functions?
What is the slope of a line that runs perfectly horizontal?
What is the slope of a line that runs perfectly horizontal?
In the function notation f(x) = 3x + 5, what is the output when the input is x = 4?
In the function notation f(x) = 3x + 5, what is the output when the input is x = 4?
If two lines are parallel, which of the following must be true?
If two lines are parallel, which of the following must be true?
Which of the following is a characteristic of continuous data?
Which of the following is a characteristic of continuous data?
The dependent variable is represented by which of the following?
The dependent variable is represented by which of the following?
How can one determine if a relation is a function?
How can one determine if a relation is a function?
Determine the slope of the line segment PQ formed by the points P(4,8) and Q(6,-3).
Determine the slope of the line segment PQ formed by the points P(4,8) and Q(6,-3).
In the equation $C = 10p + 200$, what does the value 10 represent?
In the equation $C = 10p + 200$, what does the value 10 represent?
How can you represent the cost for 30 people attending the banquet using the function $C = 10p + 200$?
How can you represent the cost for 30 people attending the banquet using the function $C = 10p + 200$?
What is the y-intercept of the function $C = 10p + 200$, and what does it represent?
What is the y-intercept of the function $C = 10p + 200$, and what does it represent?
For the function $f(x) = 2x^2 + 3x - 6$, calculate the value of $f(5)$.
For the function $f(x) = 2x^2 + 3x - 6$, calculate the value of $f(5)$.
What is the domain of the relation described in the cost of publishing books where the cost is $2000$ initially and $20$ per book after?
What is the domain of the relation described in the cost of publishing books where the cost is $2000$ initially and $20$ per book after?
Which of the following describes the relationship between cost and number of tickets in a cinema where the graph is not joined?
Which of the following describes the relationship between cost and number of tickets in a cinema where the graph is not joined?
Which of the following scenarios results in an undefined slope?
Which of the following scenarios results in an undefined slope?
Flashcards
x-intercept
x-intercept
The point where the graph crosses the x-axis. This happens when y = 0.
y-intercept
y-intercept
The point where the graph crosses the y-axis. This happens when x = 0.
Domain
Domain
The set of all possible input values (x) for a function or relation.
Range
Range
Signup and view all the flashcards
Function
Function
Signup and view all the flashcards
Function Example
Function Example
Signup and view all the flashcards
Slope
Slope
Signup and view all the flashcards
Collinear Points
Collinear Points
Signup and view all the flashcards
Slope of a line
Slope of a line
Signup and view all the flashcards
Parallel lines
Parallel lines
Signup and view all the flashcards
Perpendicular lines
Perpendicular lines
Signup and view all the flashcards
Slope formula
Slope formula
Signup and view all the flashcards
Slope of a line segment
Slope of a line segment
Signup and view all the flashcards
Rate of Change
Rate of Change
Signup and view all the flashcards
Y-intercept in a Word Problem
Y-intercept in a Word Problem
Signup and view all the flashcards
Slope in a Banquet Cost Problem
Slope in a Banquet Cost Problem
Signup and view all the flashcards
Y-intercept in a Banquet Cost Problem
Y-intercept in a Banquet Cost Problem
Signup and view all the flashcards
Relation
Relation
Signup and view all the flashcards
Study Notes
Coordinate Plane
- The origin is the point where the x-axis and y-axis intersect.
- The x-axis is the horizontal number line.
- The y-axis is the vertical number line.
- Coordinate points are always listed as (x, y).
- Quadrants are four sections of the coordinate plane.
Data
- Continuous Data: Values between data points make sense; connect the points. (e.g., Growth of a student over time)
- Discrete Data: Values between data points do not make sense; do not connect the points. (e.g., Revenue at a concert when tickets are sold for a fixed price)
Variables
- Independent Variable: Input; Domain
- Dependent Variable: Output; Range
Graphs
- Graphs are a way to represent data visually.
- Multiple types of graphs exist (scatter plots, lines, etc.).
Mappings
- Represent a relationship between inputs (domain) and outputs (range).
- Example: Shows the inputs and the respective outputs.
Equations
- Mathematical statements that show the relationship between variables represented as y = ... or f(x) = ...
Function Notation
- Special notation used for functions, like f(x) or g(x) or h(x) (specific names for the functions).
- f(2) stands for finding the output value of the function f when the input is 2.
x-intercept and y-intercept
- x-intercept: The point where the graph crosses the x-axis (when y = 0).
- y-intercept: The point where the graph crosses the y-axis (when x = 0).
Slope
- The "steepness" of a graph.
- Calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁).
- Positive slope: graph goes upward from left to right.
- Negative slope: graph goes downward from left to right.
- Zero slope: horizontal line.
- Undefined slope: vertical line.
Collinear, Parallel, and Perpendicular Lines
- Collinear points: Points that have the same slope.
- Parallel lines: Lines with the same slope and different y-intercepts.
- Perpendicular lines: Lines whose slopes are negative reciprocals of each other.
Rate of Change
- A way to describe the slope in word problems.
- Example: The cost of renting a car plus mileage charged.
Domain and Range
- Domain: The set of all possible input values (x-values).
- Range: The set of all possible output values (y-values).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz covers the fundamental concepts of the coordinate plane, including the origin, axes, quadrants, and the distinction between continuous and discrete data. Additionally, it explores variables, types of graphs, and equations that describe relationships in data. Test your understanding of these key topics!
