Questions and Answers
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
y - 1 = 1/2(x - 5)
Which equation represents a line that passes through (4, 1/3) and has a slope of 3/4?
y - 1/3 = 3/4(x - 4)
Which equation represents a line that passes through (2, -1/2) and has a slope of 3?
y + 1/2 = 3(x - 2)
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3?
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Which point did Harold use when he wrote y = 3(x - 7)?
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Which equation could represent the same line that contains the point (1, 7) and is represented by f(x) = 4x + 3?
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Which equation should Alejandra write to represent the new line after changing the slope to 2 while passing through the same point?
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What is the equation of the graphed line in point-slope form?
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What is the slope of the line Anya graphed represented by (y - 2) = 3(x - 1)?
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Which equations/functions represent the graphed line? Check all that apply.
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What is the equation of the graphed line in point-slope form?
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Which steps should be used to graph the equation y - 4 = 1/3 (x + 2)?
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Which of Talia's steps is incorrect when writing the equation of the graphed line?
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What is the equation of the graphed line in point-slope form?
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What number will complete the point-slope equation that models the newspaper circulation scenario?
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Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
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Which equation represents a line that passes through (-9, -3) and has a slope of -6?
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Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?
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What is the slope of the line?
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What is the slope of the line?
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Study Notes
Point-Slope Form of a Line
- Point-slope form of a line is represented by the equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
- Example equations derived from given points and slopes include:
- For point (5, 1) and slope 1/2: y - 1 = 1/2(x - 5)
- For point (4, 1/3) and slope 3/4: y - 1/3 = 3/4(x - 4)
- For point (2, -1/2) and slope 3: y + 1/2 = 3(x - 2)
Transforming Equations
- Changing the slope while keeping the same point results in a new point-slope equation.
- Example: Original equation y - 3 = 1/5(x - 10) changes to y - 3 = 2(x - 10) when slope changes to 2.
Identifying Points from Equations
- Equations may imply a specific point used to derive them.
- Harold's equation y = 3(x - 7) indicates he used the point (7, 0).
Graphing Lines
- The process of graphing a line includes plotting a point and using slope to find additional points.
- For the equation y - 4 = 1/3(x + 2):
- First, plot the point (-2, 4).
- Next, move left 3 units and down 1 unit to plot a second point.
- For the equation y - 4 = 1/3(x + 2):
Accessing Slope
- The slope can be easily identified from the point-slope form, such as in the equation (y - 2) = 3(x - 1) where the slope is 3.
Functions and Equations
- Linear functions can be rewritten in standard form from point-slope equations.
- An example includes transforming y + 1 = -3(x - 5) into f(x) = -3x + 14.
Assessing the Slope
- The slope can be calculated as the rise over run, a critical aspect of linear equations.
- For slope represented in various equations, common values found include -1/2 and 5/2.
Application in Real-World Scenarios
- Point-slope forms can model real-world situations, such as newspaper circulation over time, reflected by the equation y - 50,000 = -3,000(x - 10).
Multiple Representations
- Various expressions can represent the same line:
- f(x) = 0.5x + 2 and equivalent point-slope forms such as y - 1 = 0.5(x + 2).
Error Spotting in Problem Solving
- In problem scenarios, be cautious of errors in slope calculation, indicating the importance of reviewing the slope ratio accurately to ensure valid equations.
Studying That Suits You
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Description
Test your knowledge of the point-slope form of a line with these flashcards. Each card challenges you to identify the correct equation of a line given a specific point and slope. Ideal for students learning algebraic concepts in mathematics.
