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 ________.
m = 1/2; (1, 4)
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)?
y + 4 = 1/2(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).
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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?
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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 _____
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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)?
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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?
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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.
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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.
