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Questions and Answers
In the equation $y = ax + b$, what does 'a' represent?
In the equation $y = ax + b$, what does 'a' represent?
- The independent variable
- The dependent variable
- The coefficient of the independent variable (correct)
- A constant value
What does the 'b' represent in the equation $y = ax + b$?
What does the 'b' represent in the equation $y = ax + b$?
- A constant value that does not change based on x. (correct)
- The independent variable.
- The dependent variable.
- The rate of change of y with respect to x.
In a scenario where you have 30 oranges and you eat 2 oranges each day, the equation representing the number of oranges remaining (y) after x days is $y = 2x + 30$.
In a scenario where you have 30 oranges and you eat 2 oranges each day, the equation representing the number of oranges remaining (y) after x days is $y = 2x + 30$.
False (B)
Identify the independent variable in the scenario: The distance traveled (in feet) depends on the time (in seconds).
Identify the independent variable in the scenario: The distance traveled (in feet) depends on the time (in seconds).
A __________ variable is a value that affects the outcome when 'x' changes.
A __________ variable is a value that affects the outcome when 'x' changes.
Match the descriptions with the correct terms related to linear equations:
Match the descriptions with the correct terms related to linear equations:
A constant represents a fixed amount that:
A constant represents a fixed amount that:
The 'a' in the equation $y= ax + b$ represents a fixed amount that doesn't change based on 'x'.
The 'a' in the equation $y= ax + b$ represents a fixed amount that doesn't change based on 'x'.
Give an example of what the constant 'b' could represent in a real-world scenario.
Give an example of what the constant 'b' could represent in a real-world scenario.
To find 'a' in an equation derived from a table of values, one must determine the __________ of the changes in 'y' over the changes in 'x'.
To find 'a' in an equation derived from a table of values, one must determine the __________ of the changes in 'y' over the changes in 'x'.
Which of the following scenarios best represents a linear equation where the slope (a) is negative?
Which of the following scenarios best represents a linear equation where the slope (a) is negative?
The number of shopping bags you use is dependent on the number of products you buy.
The number of shopping bags you use is dependent on the number of products you buy.
What are the three steps to writing an equation from a table.
What are the three steps to writing an equation from a table.
In the equation, $y = x * 7 - 2$, to get y you must times x by 7 and ______ 2
In the equation, $y = x * 7 - 2$, to get y you must times x by 7 and ______ 2
Match the following examples with what they would be in an equation.
Match the following examples with what they would be in an equation.
What is another word for slope.
What is another word for slope.
The dependent variable changed the independent variable.
The dependent variable changed the independent variable.
What is the equation for question 4 in the image?
What is the equation for question 4 in the image?
The value that effects the outcome when x changes is attached to a ______.
The value that effects the outcome when x changes is attached to a ______.
Match the following examples with their descriptions.
Match the following examples with their descriptions.
Flashcards
Dependent Variable
Dependent Variable
The variable that is affected by changes in the independent variable.
Independent Variable
Independent Variable
The variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable.
Coefficient 'a'
Coefficient 'a'
In the equation y = ax + b, 'a' is the coefficient attached to the independent variable. It affects the outcome when 'x' changes.
Constant 'b'
Constant 'b'
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Rate of Change
Rate of Change
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Constant Value/Starting Value
Constant Value/Starting Value
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Writing Equations from Tables
Writing Equations from Tables
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Study Notes
- Review for quiz 4-8 to 4-10
- Date 4/14/2025
- Date 4/22/2025
Writing Equations
- Equation is y=ax+b
- 'y' represents the dependent variable
- 'x' represents the independent variable
- 'a' is the coefficient or rate of change
- 'b' is a constant
- 'a' is attached to an independent variable
- The value of 'a' affects the outcome when 'x' changes
- 'a' represents a rate of change. Examples: $6 per x pounds or 9mph (x hours)
- 'b' is a constant that represents a fixed amount
- 'b' doesn't change the outcome with 'x'
- Examples of 'b': entrance fee, cost of materials, or starting value
Oranges Example
- If you have 30 oranges and eat 2 each day, you can write an equation for the amount of oranges you have left
- y= -2x + 30 if 'y' equals oranges
- Minus sign indicates that something is decreasing
Distance Equation
- y = distance (ft)
- x = seconds (time)
From a Table:
- Step 1: Identify the changes in 'x' and 'y'
- Step 2: Find "a," the ratio of change in y/change in x
- Step 3: Pick any point and solve for "b"
Additional Points and Equations
- Tables show examples of how x changes in relation to y
- Example is y=x*7-8 in one table
- Example is y=(1/2)x+6
Tickets Example
- Tickets equation with x representing the number of tickets and y the cost
- 5 tickets = $12:50 or $2.50 each
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