Questions and Answers
What number will complete the point-slope equation that models the circulation scenario? y - 50,000 = [_______](x - 10)
-3,000
Which of Talia's steps is incorrect when writing the equation of the graphed line in point-slope form?
Which graph matches the equation y + 3 = 2(x + 3)?
Graph one (points (-3, -3) and (0, 3))
What is the slope of the line whose equation is y - 4 = 5/2(x - 2)?
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Which point did Harold use to write the equation y = 3(x - 7)?
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What is the slope of the line with the equation y - 3 = -1/2(x - 2)?
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Study Notes
Point-Slope Form Overview
- Point-slope form of a linear equation is expressed as ( y - y_1 = m(x - x_1) ), where ( (x_1, y_1) ) is a point on the line and ( m ) is the slope.
Example Scenarios
- The newspaper in Haventown had a circulation of 80,000 in 2000 and 50,000 in 2010. The point-slope equation for this scenario can be filled as ( y - 50,000 = -3,000(x - 10) ).
- A linear function represented by the point-slope equation ( y + 1 = -3(x - 5) ) simplifies to ( f(x) = -3x + 14 ).
Student Steps in Equation Formation
- Talia's steps to find the point-slope form were partially accurate. She correctly chose points and identified the slope; however, her slope calculation in Step 3 was incorrect.
Graphical Representations
- The graph that corresponds with the equation ( y + 3 = 2(x + 3) ) includes points (-3, -3) and (0, 3).
- Several linear functions may represent a graphed line, including ( f(x) = \frac{1}{2}x + 2 ), ( y - 3 = \frac{1}{2}(x - 2) ), and ( y - 1 = \frac{1}{2}(x + 2) ).
Slope Evaluations
- The slope of the line given by the equation ( y - 4 = \frac{5}{2}(x - 2) ) is ( \frac{5}{2} ).
- The slope from the equation ( y - 3 = -\frac{1}{2}(x - 2) ) is ( -\frac{1}{2} ).
Specific Line Equations
- Harold's equation ( y = 3(x - 7) ) indicates he used the point (7, 0).
- The equation representing a line passing through the point (4, ( \frac{1}{3} )) with a slope of ( \frac{3}{4} ) is ( y - \frac{1}{3} = \frac{3}{4}(x - 4) ).
- For a line through (-9, -3) with a slope of -6, the equation is ( y + 3 = -6(x + 9) ).
Studying That Suits You
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Description
Test your understanding of the point-slope form of linear equations with these quiz flashcards. You'll answer questions involving real-world scenarios and converting point-slope equations into linear functions. Perfect for students looking to solidify their grasp on this essential algebra concept.
