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k or constant of variation

Learn about direct variation, y-intercept, slope-intercept form, and writing equations in this comprehensive study guide. Practice problems and examples provided to enhance understanding.

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k or constant of variation

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  1. grade Time studying Introducing…. Section 5.2 Vocabulary Direct Variation • “y varies directly as x” • when y goes up, x goes up • when y goes down, x goes down • y-intercept is zero The more you study the better your grade. k or constant of variation • k is the slope y = kx

  2. (0, 5) Introducing…. Section 5.3 Vocabulary y-intercept • place where graph crosses y-axis • (0, b) Slope intercept form • m= slope • b = y-intercept, (0, b) • (x, y) = any point on the line y = mx + b

  3. Type 2 writing • Write your own situation that can be modeled using the equation y = 3.25x • Complete the table below and make a sketch of the graph of the equation. x y 0 1 2 3 0 3.25 6.50 9.75

  4. Friday’s H.W. Quiz

  5. Notes: Lesson 5-3A Objective: Write and graph slope-intercept equations

  6. For each problem, you need only 2 things: 1. y-intercept or b 2. slope or m

  7. Write an equation of the line whose slope is and whose y-intercept is –6. Slope-intercept form Replace m with and b with –6. Answer: Example 3-1a

  8. Example 3-1b Write an equation for the line with: a. slope of -3, y-intercept of 7 b. slope of 2, y-intercept of 0 c. slope of 0, y-intercept of 5 Answer: y = -3x + 7 Answer: y = 2x Answer: y = 5

  9. Example 3-2a Write an equation of the line shown in the graph. Step 1Find the slope of the line Step 2The line crosses the y-axis at (0, –3). So, the y-intercept is –3.

  10. Slope-intercept form Replace m with 2 and b with –3. Answer: The equation of the line is Example 3-2b Step 3Finally, write the equation.

  11. Answer: Example 3-2c Write an equation of the line shown in the graph. 1-3 4-0 -2 4 -1 2 m = = = b = 3

  12. Graph Step 2The slope is 0.5 or Example 3-3a Step 1The y-intercept is –7. So graph (0, –7). From (0, –7), move up 1 unit and right 2 units. Draw a dot. Step 3Draw a line connecting the points.

  13. Graph Answer: Example 3-3b Step 1The y-intercept is –4. So graph (0, –4). Step 2The slope is 2 From (0, –4), move up 2 units and right 1 unit. Draw a dot.

  14. Homework: Lesson 5-3, page 275 #14-33 (all) please do #28-33 on graph paper

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