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SLOPE of A LINE

SLOPE of A LINE. Slope. What is slope? Why do we want to know? Look at the relationship between rise and run in each of the lines. That would define the slope of the line. y. X. Line 1. Line 1. Line 2. Line 2. Look at the relationship between the blue arrow and the red arrow. =. SLOPE.

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SLOPE of A LINE

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  1. SLOPE of A LINE

  2. Slope • What is slope? • Why do we want to know? • Look at the relationship between rise and run in each of the lines. That would define the slope of the line. y X

  3. Line 1 Line 1 Line 2 Line 2 Look at the relationship between the blue arrow and the red arrow

  4. = SLOPE What is the slope of this staircases?

  5. Practice Problems #1 #2 #3

  6. Draw three different staircases that have a slope of 3/2. Label the riser and runner for each staircase.

  7. What is the slope of this staircase?

  8. What is the slope of this line?

  9. A B

  10. CHALLENGE PROBLEM: Draw a line with a slope of 3/1. Can you draw more than 1?

  11. Slope Practice A B

  12. Order these staircases from flattest to steepest (#1 is the flattest, #2 is the next flattest). If two staircases have the same slope, give them the same number. A B C D F E G { F, C, E, A/D, G, B } { .4, .666, .75, 1/1, 1.666, 4 }

  13. Special cases Horizontal Line m= 0 Vertical Line m = undefined

  14. Finding the slope given two points Find the slope of the line that passes through (2, 3) and (4, -1) Two ways to do this: • With a picture • With a formula

  15. Two ways: • Do it on a graph • Formula: m = y2-y1 x2-x1 Find the slope through (3, 2) and (-1, 5)

  16. Find the slope of the lines that contain the following points • (1, 0) and (-2, 1) • (2, 3) and (5, -2) • (3, 3) and (1, -1)

  17. The slope is the coefficient of x (you might have to solve for y first) Find the slope of the these equations: a) y = -2x + 1 m = b) 3y + 2x = -9 m = c) x - y = 4 m =

  18. Equations of lines in slope intercept formy = mx + b m = slope is the number next to x (the coefficient of x) b = the y-intercept (the point where the lines crosses the y-axis)

  19. Find the slope and the y-intercept m y-int

  20. To graph using the slope and y-intercept 1) Start on the y-axis at b 2) Use the slope m to draw the triangle (you need a fraction here) Positive m - up and right Negative m - down and right

  21. Use the slope and y-intercept to graph lines

  22. Drawing a Line with One Point & The Slope Draw the line that passes through (-1, -3) & has Slope = 4/2

  23. Example #2. Point (-4, 3) & Slope = -3/2

  24. Slope: slope m = • To find slope from two points: use the formula or draw the two points and draw the triangle. • To find slope from a graph: draw the triangle (you need to choose two points on the line first) • To find slope from an equation - solve for y first, the slope is the coefficient of x. Parallel Lines: they have the same slope Perpendicular Lines - slopes and opposites and reciprocals from each other

  25. Pos neg Sketching Lines To sketch a line you need to know: • direction: given by the sign of m B) steepness: given by the absolute value of m C) where it hits the y-axis: given by b

  26. Sketch and describe the line

  27. Parallel lines Have the same slope. Are these lines parallel? • You need the slope m • You might have to solve for y first.

  28. They are the same - just rotated The run of the first is the ____ of the second one. The rise of the first is the ____ of the second one. If the slope of the first one is m The slope of the second one is_____ Perpendicular Lines Triangles I drew to find slope

  29. Are the following lines perpendicular, parallel or neither? y = 3x + 2 and y = -3x + 4 y = 3x + 2 and y = 1/3 x + 2 y = 3x + 2 and y = -1/3 x + 2 y = 3x + 2 and y = 3x - 5 2) Find the slope of the line perpendicular and parallel to the graph of each line: y = 3/2 x + 7 y = 1 2x + y = 3 y = 3x - 2

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