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SLOPE

SLOPE. 8.2.spi11. Finding the slope of a line:. The slope of a hill means how steeply it goes up or down. Lines and curves also have a slope. To find slope: Slope = change in y change in x . Slope = change in y change in x. Graph (-4, 2) and (1,3).

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SLOPE

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  1. SLOPE 8.2.spi11

  2. Finding the slope of a line: • The slope of a hill means how steeply it goes up or down. Lines and curves also have a slope. • To find slope: • Slope = change in y change in x

  3. Slope = change in y change in x Graph (-4, 2) and (1,3) Slope = 1 5

  4. The slope of a line through (-4,2) and (1,3) is 1/5. • Go from the left point to the right point you count 1 up and 5 across. • Slope = change in y = 1 change in x = 5

  5. Finding Slope of a Line • Designate two points as : (x ,y ) and (x ,y ) • Formula for calculating the slope between two points: • Slope = y -y x -x The formula really means: Slope = the difference of the y-coordinates the difference of the x-coordinates

  6. Example • Find the slope of the line through (-4,2) and (1,3). • Use the slope formula: = y -y x -x = 3 -2 1-(-4) = 1/5

  7. (3,5) What is the slope of this line? (2,3) (1,1) (0,-1) (-1,-3)

  8. How to find slope: • Pick any two coordinates: • I picked (2,3) and (3,5) • Slope = 5-3 = 2 = 2 3-2 1 ** If a graph is given to you without coordinates, then estimate what the coordinates would be. Then just plug in your coordinates into the slope formula. Remember that the coordinates can be ANYWHERE on the line!!

  9. Find the slope of y = 3x – 4 Let x be zero and two. Then calculate the corresponding y-coordinates. With those two points, you can graph the line and calculate the slope. First, make a graph with the number 0 and 2 being x. Finding slope Using its Equation

  10. (2,2) • The points are • (0,-4) and (2,2) (0,-4)

  11. Solve for the slope: • Now put the coordinates into the slope formula to solve: • (0,-4) and (2,2) • 2 – (-4) = 6 = 3 2 – 0 2

  12. Short-Cut! • A short-cut for finding slope from an equation: • y = 3x – 4 (this was our equation) • y = mx + b (this is the same equation without numbers) • The number with “x” is the slope! The other number is just where the slope lays on the y axis. • So the slope in the equation y = 3x – 4 is simply 3.

  13. Horizontal lines have a slope of zero • Vertical lines have no slope m = 0 Vertical Horizontal m = no slope

  14. Slope-Intercept Form: y = 2x + 4 Standard Form: -2x + y = 4

  15. Intercepts • X-intercept – point at which the line crosses the x-axis • To find the x-intercept, plug in 0 for y • Y-intercept – point at which the line crosses the y-axis • To find the y-intercept, plug in 0 for x

  16. Slope intercept form is: y = mx + b Our main goal is to get the y alone on one side of the equation

  17. Convert Into Slope-Intercept Form (divide both sides by 2 to get y alone) (now simplify all fractions) 2 1

  18. Intercept slope Now look at the equation below…… When an equation is in slope-intercept form: y = mx + b 2 What is the slope? ____________ 1 What is the intercept? ____________

  19. *** Easy *** Convert to Slope-Intercept Form: 5y = 10x + 15 (divide both sides by 5 to get y alone) (now simplify all fractions) y = 2x + 3 BRAVO!!

  20. *** Now Try this Convert to Slope-Intercept Form*** -3y = -9x - 12 Step 1: divide both sides by -3 to get y alone Step 2: Simplify all fractions Step 3: Write your equation in y = mx + b What is the slope? ____________ What is the intercept? ____________

  21. -3-3 -3y = -9x - 12 -3-3 -3 *** Check Your Answer *** -3y = -9x - 12 (divide both sides by -3 to get y alone) (now simplify all fractions) y = 3x + 4 Wow, you’re good at this!! Slope = 3 Intercept = 4

  22. *** Now Try this Convert to Slope-Intercept Form*** 2y + 26 = -6x Step 1: Subtract both sides by 26 Step 2: Divide both sides by 2 to get y by itself Step 3: Simplify all fractions What is the slope? ____________ What is the intercept? ____________

  23. *** Check Your Answer*** 2y + 26 = -6x (subtract both sides by 26) (now divide both sides by 2 2y = -6x - 26 (simplify all fractions) y = -3x - 13 You are a math wizard!

  24. Example Using 4x – 2y = 12, what is the slope and the intercepts?

  25. X-intercept: 4x – 2(0) =12 4x=12 X=3 Y-intercept 4(0) -2y=12 -2y=12 Y=-6 Slope: Use the intercepts to find the slope (3,0) and (0,-6) Change in y: -6-0=-6 Change in x: 0-3 = -3 M= -6 = 2 3 Answer

  26. Write the equation of a line that has a y-intercept of -3 and a slope of -4. • y = -3x – 4 • y = -4x – 3 • y = -3x + 4 • y = -4x + 3

  27. Write an equation of the line that goes through the points (0, 1) and (1, 4). • y = 3x + 4 • y = 3x + 1 • y = -3x + 4 • y = -3x + 1

  28. Find the slope and y-intercept of y = -2x + 4 • m = 2; b = 4 • m = 4; b = 2 • m = -2; b = 4 • m = 4; b = -2

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