Podcast
Questions and Answers
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
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?
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?
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?
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)?
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?
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?
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?
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)?
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.
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?
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)?
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?
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?
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?
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?
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?
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)?
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?
What is the slope of the line?
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What is the slope of the line?
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
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
