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Slope and Stuff

Slope and Stuff. First, Some Important slides from last time! Take Some Notes!. Y-int. Slope. Slope Intercept Form for a Line with a Slope of m and a y-intercept of b is…. Slope describes a lines its steepness, incline, decline or grade. = Change in y =. = Change in x =. What the Slope?.

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Slope and Stuff

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  1. Slope and Stuff First, Some Important slides from last time! Take Some Notes!

  2. Y-int. Slope • Slope Intercept Form for a Line with a Slope of m and a y-intercept of b is… Slope describes a lines its steepness, incline, decline or grade. = Change in y = = Change in x =

  3. What the Slope? Slope describes a lines its steepness, incline, decline or grade. = Change in y = = Change in x =

  4. How do we calculate Slope With 2 Points? If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope? Change in y (rise) over the Change in x (run). It looks likes this. (x2, y2) (x1, y1)

  5. Example #1 If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope? (x2, y2) (3, 3) (x1, y1) (0, 0) = m

  6. Example #2 If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope? (x2, y2) (3, 1) = m = (1, -2) (x1, y1)

  7. Example #3 If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope? (x1, y1) (-2, 1) = = (x2, y2) (2, -2) = m

  8. m = Using Example #1 What is the y intercept? How do we find it? Our equation is y = x + b (remember m = 1) We have 2 Points! (3,3) and (0,0). Lets just plug one of them into our equation. Which is easiest? (x2, y2) (3, 3) (x1, y1) (0, 0) y = x + b 0 = 0 + b (0,0) 0 = b So… y = x + 0 or… y = x!!

  9. Find the y-int of example #2 Our two points = = m (3, 1) (1, -2) (x2, y2) Our equation (3, 1) What point to plug in? (3, 1) (1, -2) (1, -2) (x1, y1)

  10. What is our equation for (3, 1) and (1,-2) then? = m Yay! Yay! Yay! Yay! Yay! Yay! Yay! Yay! Yay!

  11. Lets talk about the x-intercept! So the y-intercept is where the line goes through the y axis, so the x-intercept is when Our line goes through the x axis. They go through points: Our y-int. (0,1) Our x-int. (-1,0) Interesting… so y is zero for the x-int! Lets find the x-intercept for an equation!

  12. Example #4 Find the x-intercept of: (x,0) y = x + 5 0 = x + 5 -x -x -x = 5 x = -5 Lets find the x-intercept for a harder equation!

  13. Example #5 Find the x-intercept of: (x,0) y = -0.5x - 3 0 = -0.5x -3 +0.5x +0.5x 0.5x = -3 /0.5 /0.5 x = -6 Is our x-intercept! (-6,0)

  14. Vertical/Horizontal Line Discussion What is the x-intercept of this vertical line? It’s -3!! So when y = 0, x = -3! What about when y = 2? It’s also -3! It’s -3 everywhere! So, x is not dependant on y, Therefore our equation of the line is x = -3

  15. Vertical/Horizontal Line Discussion What is the y-intercept of our vertical line? Our equation of the line is x = -3 So, there will be no y-int Sorry y-int…

  16. Vertical/Horizontal Line Discussion What is the slope of our vertical line x = -3? Let’s think about rise over run first. Can’t divide be zero… Lets try 2 points, (-3,2) and (-3,0) Can’t divide be zero

  17. Vertical/Horizontal Line Discussion What is the slope of our vertical line x = -3? our slope is Undefined. All vertical lines have an undefined slope. Sorry slope

  18. Vertical/Horizontal Line Discussion What is the x-int and y-int of a horizontal line? y-int is 3. in fact, its 3 everywhere! x-int does not exist. So y = 3

  19. Vertical/Horizontal Line Discussion What is the slope of a horizontal line y = 3? Let’s think about rise over run first. Cool… Lets try 2 points, (1,3) and (2,3)

  20. Vertical/Horizontal Line Discussion What is the slope of our horizontal line y = 3? our slope is 0. All horizontal lines have a zero slope.

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