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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)?
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?
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?
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?
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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)?
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What does the x-intercept of a graph represent?
What does the x-intercept of a graph represent?
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Which of the following characteristics is true for functions?
Which of the following characteristics is true for functions?
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What is the slope of a line that runs perfectly horizontal?
What is the slope of a line that runs perfectly horizontal?
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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?
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If two lines are parallel, which of the following must be true?
If two lines are parallel, which of the following must be true?
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Which of the following is a characteristic of continuous data?
Which of the following is a characteristic of continuous data?
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The dependent variable is represented by which of the following?
The dependent variable is represented by which of the following?
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How can one determine if a relation is a function?
How can one determine if a relation is a function?
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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).
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In the equation $C = 10p + 200$, what does the value 10 represent?
In the equation $C = 10p + 200$, what does the value 10 represent?
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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 $C = 10p + 200$?
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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?
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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 $f(5)$.
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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?
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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?
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Which of the following scenarios results in an undefined slope?
Which of the following scenarios results in an undefined slope?
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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).
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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!
