Questions and Answers
What is the slope formula?
y2 - y1/x2 - x1
What is the point slope form?
y - y1 = m(x - x1)
What is the slope intercept form?
y = mx + b
What is the direct variation formula?
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What does k stand for in the direct variation equation?
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Every direct variation graph goes through what?
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Write an equation in point slope form through the point (5, 1) and has a slope of m = 1/3.
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Write an equation in point slope form through the point (-2, 3) and has a slope of m = -2.
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What are the two things that standard form helps you find?
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Graph the equation y = 4x - 4.
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Graph the equation y = -x - 2.
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Does the equation 2x + 3y = 0 represent direct variation?
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Does the equation 4x + 6y = 3 represent direct variation?
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Find the slope of the points (1, 1) and (10, 5).
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Find the slope of the points (5, 9) and (2, 4).
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Give an example of a positive slope.
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Give an example of a negative slope.
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What is 0 slope?
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What is undefined slope?
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The slope of a line is positive, negative, or zero?
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Study Notes
Slope Concepts
- Slope formula is calculated as ( \frac{y_2 - y_1}{x_2 - x_1} ).
- Point-slope form is expressed as ( y - y_1 = m(x - x_1) ).
- Slope-intercept form is given as ( y = mx + b ).
Direct Variation
- Direct Variation formula is ( y = kx ), where ( k ) represents the constant of variation.
- Every Direct Variation graph passes through the origin (0,0).
Point-Slope Form Equations
- Example equation through point (5, 1) with slope ( \frac{1}{3} ) is ( y - 1 = \frac{1}{3}(x - 5) ).
- Example equation through point (-2, 3) with slope -2 is ( y - 3 = -2(x + 2) ).
Standard Form Applications
- Standard form assists in determining the x and y intercepts of a line.
Graphing Examples
- Graphing the equation ( y = 4x - 4 ).
- Graphing the equation ( y = -x - 2 ).
Direct Variation Verification
- The equation ( 2x + 3y = 0 ) represents Direct Variation.
- The equation ( 4x + 6y = 3 ) does not represent Direct Variation.
Slope Calculations
- The slope between points (1, 1) and (10, 5) is ( \frac{4}{9} ).
- The slope between points (5, 9) and (2, 4) is ( \frac{5}{3} ).
Slope Characteristics
- Positive slope indicates a line that rises from left to right.
- Negative slope indicates a line that falls from left to right.
- Zero slope indicates a horizontal line with no vertical change.
- Undefined slope indicates a vertical line with no horizontal change.
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Description
Test your understanding of key concepts in Algebra 1, Chapter 5. This quiz covers essential formulas such as slope formula, point slope form, and direct variation. Use this review to prepare for upcoming exams and strengthen your algebra skills.
