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Equations of Lines: Slope and Intercepts Formulas, Point-Slope Form, Standardized Test Practice

Learn to write equations of lines and solve problems using slope, intercept, and point-slope forms. Practice graphing, identifying slopes, and determining relationships between points. Includes vocabulary and sample problems for reinforcement.

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Equations of Lines: Slope and Intercepts Formulas, Point-Slope Form, Standardized Test Practice

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  1. Lesson 3-4 Equations of Lines

  2. Transparency 3-4 5-Minute Check on Lesson 3-3 Find the slope of each line for M(–3, 4) and N(5, –8). 1. MN 2. a line perpendicular to MN 3. a line parallel to MN Graph the line that satisfies each condition. 4. slope = 4 and 5. slope = 0 and contains (1, 2) contains (–3, –4) 6. Use slope to find a relationship between CD and EF for C(4, 5), D(–1, 15), E(–4, –6), F(0, –8). –3/2 2/3 –3/2 Standardized Test Practice: A B CD || EF CD  EF C C neither || nor  D not enough information given

  3. Objectives • Write an equation of a line given information about its graph • Solve problems by writing equations

  4. Vocabulary:Equations of Lines • Slope – Intercept Form: y = mx + b • Point Slope Form: y – y1 = m(x – x1) • From two points: (y2 – y1) y – yp = –––––––– (x – xp) (x2 – x1) m is the slope b is the y-intercept m is the slope (x1,y1) is the given point (y2 – y1) / (x2 – x1) is the slope p is one of the given points

  5. Answer: The slope-intercept form of the equation of the line is Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Slope-intercept form

  6. Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Point-slope form Simplify. Answer:

  7. Write an equation in point-slope form of the line whose slope is that contains (6, –3). Answer:

  8. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0). Find the slope of the line. Slope formula Simplify.

  9. Now use the point-slope form and either point to write an equation. Using (4, 9): Point-slope form Distributive Property Add 9 to each side.

  10. Using (–2, 0): Point-slope form Simplify. Distributive Property Answer:

  11. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8). Answer:

  12. Write an equation in slope-intercept form for a line containing (1, 7) that is perpendicular to the line the slope of a line perpendicular to it is 2. Point-slope form Distributive Property Add 7 to each side.

  13. Write an equation in slope-intercept form for a line containing (–3, 4) that is perpendicular to the line Answer:

  14. Answer: The total annual cost can be represented by the equation RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Write an equation to represent the total annual cost A for r months of rent. For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750. Slope-intercept form

  15. First complex: Second complex: Simplify. RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Compare this rental cost to a complex which charges a $200 security deposit but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate? Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.

  16. RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. a. Write an equation to represent the total cost C for d days of use. b. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate? Answer: Answer: The first company offers the better rate. Nine days cost $325 instead of $365.

  17. Summary & Homework • Summary: • An equation of a line can be written if you are given: • The slope and the y intercept, or • The slope and the coordinates of a point on the line, or • The coordinates of two points on the line • Homework:pg 148-149: 15-19, 21, 35, 37, 47

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