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Point Slope

Point Slope. Math 374. Topic Box. 1) Slope 2) Word Problems - keys - Point – Point - Slope – Point - Y Int – Point - Slope – Y int. The Slope. We know that we are dealing with linear functions y = mx + b. y int. Slope.

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Point Slope

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  1. Point Slope Math 374

  2. Topic Box • 1) Slope • 2) Word Problems - keys - Point – Point - Slope – Point - Y Int – Point - Slope – Y int

  3. The Slope • We know that we are dealing with linear functions y = mx + b y int Slope The slope is not always obvious, if we do not know the equation

  4. Understanding the Slope • What makes a slope? • We define the slope as the ratio between the rise and the run Rise • Slope = m = rise • run Run

  5. Formula for Slope • If we have two points (x1, y1) (x2, y2) • Slope = m = y1 – y2 = y2 – y1 x1 – x2 x2 – x1 • Remember it is Y over X! • Maintain order

  6. (x1,y1) (x2,y2) Calculating Slope • Slope = m = y1 – y2 = y2 – y1 x1 – x2 x2 – x1 (5, 4) (2, 1) • 4 - 1 • 5 - 2 • 3 • 3 • m = 1

  7. Ex # 2 A = (-4, 2) B=(2, -4) (x1,y1) (x2,y2) • -4 – 2 • 2 - - 4 • 6 • 6 • m = -1

  8. Ex #3 (4, 5) (x1,y1) (1, 1) (x2,y2) 1 – 5 1 – 4 m = -4 -3

  9. Two Decimal Place Practice • Find the slope of (4,217.08) (11,575.41) • m = 217.08 – 575.41 4-11 • 51.19

  10. Word Problems BASICS • Set your x and y • Find the linear function meaning find slope – m and y int or b • Solve question • x is always time • y is always money

  11. Word Problems Con’t KEYS • Per • Rate m • Fixed • Initial b Point – two values point

  12. Point – Point • Little Billy rents a car for 5 days and pays $463.65. Little Sally rents a car for 14 days and pays $1208.22 • How much would it cost to rent a car for 27 days? • How many days can you get for $2531.90 Step 1: Set Your x and y… what are they?

  13. Solution • x is # of days • y is $ (money) • (5, 463.65) (14, 1208.22) • m = 463.65 – 1208.22 5 – 14 • m = 82.73 • y = 82.73x + b

  14. Solution Con’t • (5, 463.65)  463.65 = 82.73(5) + b • 463.65 = 413.65 + b • 50 = b • b = 50 • y = 82.73x + 50 • A) x = 27  y = 82.73 (27) + 50 • y = $2283.71

  15. Solution Con’t • b) y = 2531.90  2531.90 = 82.73x + 50 • 2481.90 = 82.73x • 30 = x • x = 30

  16. Slope Point • Little Billy rents a car and pays a rate of $43.91 per day. Little Sally rents for 42 days and pays $1900.45 • a) How much would it cost to rent a car for 27 days? • b) How many days can you get for $2471.28? • Step 1: Set your x and y

  17. Solution • x is # of days • y is $ (money) • m = $43.91 (42,1900.45) • y = 43.91x + b • (42,1900.45)  1900.45 = 43.91 (42) + b • 1900.45 = 1844.22 + b • 56.23 = b • b = 56.23

  18. Solution Con’t • y = 43.91x + 56.23 • A) x = 27  y = 43.91 (27) + 56.23 • y = $1241.80 • B) y = 2471.28  2471.28=4391 x+56.23 • 2415.05 = 43.91x • 55 = x • x = 55

  19. Y Int - Point • Little Billy rents a car and pays a fixed cost of $132.11. Little Sally rents for 12 days and pays $1331.99 • a) How much for 27 days? • b) How many days for $1232? • x is # of days • y is $ money • b = 132.11 (12, 1331.99) • y = mx + 132.11

  20. Solution • (12, 1331.99)  1331.99 =12m+132.11 • 1199.88 = 12m • 99.99 = m • m = 99.99 • y = 99.99x + 132.11 • a) x = 27  y = 99.99 (27) + 132.11 • y = $2831.84

  21. Solution (Con’t) • B) y = 1232  1232 = 99.99x + 132.11 • 1099.89 = 99.99x • 11 = x • x = 11

  22. Slope – Y int • Little Billy rents a car and pays a rate of $73.99 per day. Little Sally pays a fixed cost of $42.19 • a) How much for 27 days? • b) How many days for $412.14 • x is # of days • y is $ (money) • m = 73.99 b = 42.99 • y = 73.99x + 42.19

  23. Solutions • x= 27  y = 73.99 (27) + 42.19 • y = 2039.92 • b) y = 412.14  412.14 = 73.99x+42.19 • 369.95 = 73.99x • 5 = x • x = 5

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