Podcast
Questions and Answers
Which graph represents this equation -3x + 4y = -12?
Which graph represents this equation -3x + 4y = -12?
- (0, -3) and (4, 0) (correct)
- (-3, -3) and (-3, 3)
- (0, 2) and (1, -3)
- (-4, 1) and (-3, -2)
The slope of the graphed line is positive.
The slope of the graphed line is positive.
True (A)
Which graph represents this equation y − 4 = -3(x + 5)?
Which graph represents this equation y − 4 = -3(x + 5)?
- (0, 2) and (1, -3)
- (-4, 1) and (-3, -2) (correct)
- (-3, -3) and (-3, 3)
- (0, -3) and (4, 0)
What is the slope of the line that goes through the points (1, -5) and (4, 1)?
What is the slope of the line that goes through the points (1, -5) and (4, 1)?
Which number best represents the slope of the graphed line?
Which number best represents the slope of the graphed line?
Graph the line that represents this equation: y = -5x + 2, the points are: (0, 2) and (1, ___)
Graph the line that represents this equation: y = -5x + 2, the points are: (0, 2) and (1, ___)
Which two points have an undefined slope?
Which two points have an undefined slope?
Determine which graph and which equation represent the amount of money Chelsea earns in one day, A, after taking w walks with the dogs.
Determine which graph and which equation represent the amount of money Chelsea earns in one day, A, after taking w walks with the dogs.
What is the equation of the line that has a slope of 3 and goes through the point (-3, -5)?
What is the equation of the line that has a slope of 3 and goes through the point (-3, -5)?
What is the slope of the line shown in the graph of the concert ticket sales?
What is the slope of the line shown in the graph of the concert ticket sales?
Which graph represents the balance of the cash box, y, after Jackie sells x smoothies?
Which graph represents the balance of the cash box, y, after Jackie sells x smoothies?
Which equation represents the height of fudge brownies with x teaspoons of baking powder?
Which equation represents the height of fudge brownies with x teaspoons of baking powder?
Which equation describes the line graphed above?
Which equation describes the line graphed above?
What is the range of the relationship between Charlotte and Travis's employment years?
What is the range of the relationship between Charlotte and Travis's employment years?
If the graph of f(x) = x is shifted up 9 units, what would be the equation of the new graph?
If the graph of f(x) = x is shifted up 9 units, what would be the equation of the new graph?
What is the y-intercept of g for the functions f(x) = -3x - 5 and g(x) = f(x) + 9?
What is the y-intercept of g for the functions f(x) = -3x - 5 and g(x) = f(x) + 9?
Graph the line representing function g, if g is defined as g(x) = f(x) + 4.
Graph the line representing function g, if g is defined as g(x) = f(x) + 4.
Which statement correctly describes the graph of function g if g(x) = -8f(x)?
Which statement correctly describes the graph of function g if g(x) = -8f(x)?
Consider the function g, which has a y-intercept of -2. Which of the following functions could represent g?
Consider the function g, which has a y-intercept of -2. Which of the following functions could represent g?
Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?
Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?
Flashcards
Slope of a line through (1, -5) and (4, 1)
Slope of a line through (1, -5) and (4, 1)
The slope is calculated as (change in y)/(change in x), which is (1 - (-5))/(4 - 1) = 6/3 = 2
Equation of a line with slope 3 and point (-3, -5)
Equation of a line with slope 3 and point (-3, -5)
Using the point-slope form, y - (-5) = 3(x - (-3)) simplifies to y + 5 = 3(x + 3), which further simplifies to y = 3x + 4
Graph of -3x + 4y = -12
Graph of -3x + 4y = -12
The graph passes through (0, -3) and (4, 0).
Slope of a line through (0, 12) and (8, 32) in a real-world context
Slope of a line through (0, 12) and (8, 32) in a real-world context
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Graph of y = -5x + 2
Graph of y = -5x + 2
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Undefined slope
Undefined slope
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g(x) = f(x) + 9, y-intercept
g(x) = f(x) + 9, y-intercept
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g(x) = f(x) + 4
g(x) = f(x) + 4
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g(x) = -8f(x)
g(x) = -8f(x)
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Vertical stretch of f(x)
Vertical stretch of f(x)
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g(x) = f(x) - 3
g(x) = f(x) - 3
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Slope of a line in a concert ticket sales graph
Slope of a line in a concert ticket sales graph
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y-intercept in g(x) = f(x) -3
y-intercept in g(x) = f(x) -3
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Range
Range
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Study Notes
Linear Relationships and Graphs
- The equation -3x + 4y = -12 is represented by graph points (0, -3) and (4, 0).
- Positive slope indicates that as x increases, y also increases.
Slope Calculations
- The slope of a line through points (1, -5) and (4, 1) is calculated as 2.
- A slope of -5 signifies a decreasing function.
Graphing Lines
- For the equation y = -5x + 2, key points are (0, 2) and (1, -3).
- An undefined slope occurs with vertical lines, exemplified by points (-3, -3) and (-3, 3).
Real-world Applications
- Chelsea earns money based on a formula A = 2.5w + 12, indicated by graph points (8, 32) and (0, 12).
- Jackie’s cash box balance after selling x smoothies can be represented with points (0, 15) and (4, 30).
Equation Representation
- The fudge brownie height relationship is expressed by y = 0.28x + 0.75 based on baking powder measurements.
- The equation y = -1/5x - 4 represents a specific graph line.
Relationship Analysis
- Travis has worked 3 years more than Charlotte, establishing a direct relationship between their work durations.
- The new equation after shifting f(x) = x up 9 units becomes g(x) = f(x) + 9.
Function Transformation
- The y-intercept of g, derived from f(x) = -3x - 5 adjusted by +9, requires calculation.
- g(x) = f(x) + 4 reflects a vertical shift upward of function f.
Vertical Shifts and Translations
- A transformation represented by g(x) = -8f(x) indicates reflection and vertical stretch.
- A y-intercept of -2 for function g suggests a downward shift, expressed as g(x) = f(x) - 5.
- The transformation g(x) = f(x) - 3 indicates a downward translation of 3 units from f(x).
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