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Lesson on Equations in Slope-Intercept and Point-Slope Forms

This lesson covers writing equations in slope-intercept and point-slope forms, as well as finding equations of parallel and perpendicular lines. It includes examples and practice questions.

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Lesson on Equations in Slope-Intercept and Point-Slope Forms

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 2–3) CCSS Then/Now New Vocabulary Key Concept: Slope-Intercept Form Example 1: Write an Equation in Slope-Intercept Form Key Concept: Point-Slope Form Example 2: Write an Equation Given Slope and One Point Example 3: Standardized Test Example Key Concept: Parallel and Perpendicular Lines Example 4: Write an Equation of a Perpendicular Line Lesson Menu

  3. A.–22 mi/gal B.mi/gal C.mi/gal D.22 mi/gal Find the rate of change for the data. 5-Minute Check 1

  4. A.–7 B. C.7 D. Find the slope of the line that passes through points (2.3, 9.5) and (3.8, 20). 5-Minute Check 2

  5. Find the slope of the line that passes through points (3, 5) and (–6, 5). A. –1 B. 0 C. 1 D. 3 5-Minute Check 3

  6. A.–3 B. C. D.3 Determine the rate of change of the graph. 5-Minute Check 4

  7. A. 72 cm B. 108 cm C. 432 cm D. 648 cm 5-Minute Check 5

  8. Content Standards A.SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity. A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Mathematical Practices 2 Reason abstractly and quantitatively. CCSS

  9. You determined slopes of lines. • Write an equation of a line given the slope and a point on the line. • Write an equation of a line parallel or perpendicular to a given line. Then/Now

  10. slope-intercept form • point-slope form • parallel • perpendicular Vocabulary

  11. Concept 1

  12. • • Write an Equation in Slope-Intercept Form Write an equation in slope-intercept form for the line. Step 1 Find the slope. Slope formula (x1, y1) = (–1, 4), (x2, y2) = (2, 3) Simplify. Example 1

  13. Slope-intercept form Simplify. The y-intercept is Write an Equation in Slope-Intercept Form Step 2 Use the slope and a point to find the y-intercept. Example 1

  14. Slope-intercept form Write an Equation in Slope-Intercept Form Step 3 Substitute the values into the slope-intercept equation. Example 1

  15. A. B. C. D. Write an equation in slope-intercept form for the line. Example 1

  16. Concept 2

  17. Point-slope form Simplify. Write an Equation Given Slope and One Point Example 2

  18. Subtract 2 from each side. Answer: Write an Equation Given Slope and One Point Example 2

  19. A. B. C. D. Example 2

  20. A B C D What is an equation of the line through (2, –3) and (–3, 7)? Read the Test Item You are given the coordinates of two points on the line. Example 3

  21. Slope formula (x1, y1) = (2, –3), (x2,y2) = (–3, 7) Simplify. Solve the Test Item Step 1 Find the slope of the line. The slope is –2. That eliminates choices B and C. Example 3

  22. Point-slope form m = –2; (x1, y1) = (2, –3) Simplify. Subtract 3 from each side. Step 2 Write an equation. Use either ordered pair for (x1, y1). Answer: D Example 3

  23. A. B. C. D. Which is an equation of the line that passes through (2, 5) and (–1, 3)? Example 3

  24. Concept

  25. Write an Equation of a Perpendicular Line Write an equation in slope-intercept form for the line that passes through (3, –2) and is perpendicular to the line whose equation is y = –5x + 1. Example 4

  26. Point-slope form Distributive Property Subtract 2 from each side. Answer: Write an Equation of a Perpendicular Line Example 4

  27. A. B. C. D. Example 4

  28. End of the Lesson

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