Podcast
Questions and Answers
Use the point-slope equation to identify the slope and the coordinates of a point on the line y - 4 = 1/2 (x - 1). The slope of the line is ______. A point on the line is ________.
Use the point-slope equation to identify the slope and the coordinates of a point on the line y - 4 = 1/2 (x - 1). The slope of the line is ______. A point on the line is ________.
m = 1/2; (1, 4)
Which point-slope equation represents a line that passes through (3, -2) with a slope of -4/5?
Which point-slope equation represents a line that passes through (3, -2) with a slope of -4/5?
y + 2 = -4/5(x - 3)
What is the equation of the line in point-slope form for y + 4 = (x + 4)?
What is the equation of the line in point-slope form for y + 4 = (x + 4)?
y + 4 = 1/2(x + 4)
Which graph represents the function y - 3 = 3/2(x - 4)?
Which graph represents the function y - 3 = 3/2(x - 4)?
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Choose a linear function for the line represented by the point-slope equation y - 5 = 3(x - 2).
Choose a linear function for the line represented by the point-slope equation y - 5 = 3(x - 2).
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Use the graph of the line to answer the questions. What is an equation of the line in point-slope form? How can the point-slope form be written in function notation?
Use the graph of the line to answer the questions. What is an equation of the line in point-slope form? How can the point-slope form be written in function notation?
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What is the y-intercept of the graphed linear function?
What is the y-intercept of the graphed linear function?
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Use the graph to find the x-intercept for the equation y + 2 = 2(x + 3). The x-intercept is _____
Use the graph to find the x-intercept for the equation y + 2 = 2(x + 3). The x-intercept is _____
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Did Andy make an error in his steps for writing the equation of a line with a slope of 3/4 through the point (3, -2)?
Did Andy make an error in his steps for writing the equation of a line with a slope of 3/4 through the point (3, -2)?
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How much did the bicycle cost? After how many weeks will Hugo finish paying for the bike?
How much did the bicycle cost? After how many weeks will Hugo finish paying for the bike?
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Which function describes the revenue of the tile factory in terms of tiles sold? What is the flat fee for delivery?
Which function describes the revenue of the tile factory in terms of tiles sold? What is the flat fee for delivery?
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Study Notes
Point-Slope Form of a Line
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The point-slope form is expressed as y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line and m denotes the slope.
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For the equation y - 4 = 1/2(x - 1):
- The slope (m) is 1/2.
- A specific point on the line is (1, 4).
Finding Point-Slope Equations
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To express a line passing through the point (3, -2) with a slope of -4/5, the equation is y + 2 = -4/5(x - 3).
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A given expression y + 4 = (x + 4) can also be written as y + 4 = 1/2(x + 4) in point-slope format.
Graphing and Identifying Lines
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The function represented by y - 3 = 3/2(x - 4) is depicted correctly by Graph One.
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The linear function derived from the point-slope equation y - 5 = 3(x - 2) is f(x) = 3x - 1.
Analyzing Graphs
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From a graphed linear function, an equation in point-slope form can be written as y + 2 = (1/3)(x + 1) and converted to function notation as f(x) = (1/3)x - (1/3).
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The y-intercept of the graphed linear function is located at the coordinates (0, 4).
Finding Intercepts
- The x-intercept for the equation y + 2 = 2(x + 3) is found to be (-2, 0).
Error Analysis in Function Notation
- In Andy's equation with a slope of 3/4 through the point (3, -2), an error occurs in Step 3:
- He should have subtracted 2 from both sides instead of adding.
Real-World Applications
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Hugo's payment plan for a bicycle, described by the equation y - 10 = -2(x - 10), indicates that the bicycle costs $30 and will take 15 weeks to pay off if he pays $2 weekly.
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A tile factory's revenue, modeled by y - 3,000 = 0.25(x - 10,000), shows:
- The revenue function can be expressed as f(x) = 0.25x + 500.
- A flat delivery fee for the factory is $500, based on a total payment of $3,000 for 10,000 tiles.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of the point-slope form of a line with these flashcards. Each card presents a scenario where you'll identify slopes, points on the line, and the correct equations. Perfect for reinforcing your knowledge of this essential algebra concept.
