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Precalculus Day #5

Precalculus Day #5. Mr. Ueland 1 st Period Rm 162. Today in Precalculus. Announcements Prayer Correct Assignment #3 [P.3, pp28-30, 1-9 odd, 21-33 odd, 37,41,49,55,66,72,73] “New” material: “Lines in the Plane”. 55. Equations and tables. 55. x 2 – 2x < 0.

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Precalculus Day #5

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  1. Precalculus Day #5 Mr. Ueland 1st Period Rm162

  2. Today in Precalculus • Announcements • Prayer • Correct Assignment #3 [P.3, pp28-30, 1-9 odd, 21-33 odd, 37,41,49,55,66,72,73] • “New” material: “Lines in the Plane”

  3. 55.Equations and tables 55. x2 – 2x < 0 Enter as an equation using F1 View as a table using <2nd> F5 Scanning the table we notice that the only value of x that yields a negative y is x = 1

  4. Review • Which of the following equations is equivalent to –3x < 6? • 3x < –6 • x < 10 • x > –2 • x > 2 • x > 3

  5. Review • Which of the following equations is the solution to the equation x(x+1) = 0? • x = 0 or x = –1 • x = 0 or x = 1 • only x = –1 • only x = 0 • only x = 1

  6. Review[What they’re working on next door] • Which of the following equations is the solution to the equation –3x ≥ 0? • x = 0 • x ≥ 0 • x ≤ 0 • x ≤ –⅓ • x is indeterminate (cannot be determined) Things get weird if you multiply both sides by zero, but not so much if you multiply zero on one side

  7. P.3: Lines in the Plane Definitions • The slope of a nonvertical line through the points (x1, y1) and (x2, y2) is • A vertical line has no slope. • A horizontal line has zero slope “rise over run” Why? Zero in the denominator is undefined

  8. The Many Forms of Equations of a Line • General form: • Point-slope form: A and B cannot BOTH be 0

  9. Forms of Equations of a Line (cont). • Point-slope form: • 2-Point form:

  10. Example 2 • Find the equation of the line with slope 2 and passing through point (–3,–4)

  11. Parallel and Perpendicular Lines • Two nonvertical lines are parallelif and only if (iff) their slopes are equal. • Two nonvertical lines are perpendicular iff their slopesm1 and m2 are opposite reciprocals:

  12. Example 6 • Find the equation of the line through P(2,–3) that is perpendicular to the line L with equation 4x + y = 3. Find the slope from the definition of a perp. line Use point-slope form

  13. Example 6 (cont.)

  14. Example 7Applications: Everybody’s favorite! Camelot Apartments purchased a $50,000 building [either this book is old or a double-dip recession is coming] and depreciates it $2000 per year over a 25-year period. Write a linear equation giving the value y of the building in terms of the years x after the purchase. In how many years will the value of the building be $24,500?

  15. Example 7 (cont.) This is a linear equation! Let y equal the value of the building, let the slope be the change of value (i.e. depreciation) and let b be the initial value (value today) NOTE: slope is negative. Why? That is your answer to part a)

  16. Example 7 (cont.) We’ll use are answer to part a) to find an answer for part b), the number of years (x) when the value of the building (y) is $24,500.

  17. Assignment 4 • P.4, pp 40-43, 1-7 odd, 11-25 odd, 37,41,45 (each part one problem), 48 • Due Monday at the start of class

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