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5.4 Point-Slope Form:

Parent Graph: Simplest function of a family of functions with common characteristics. 5.4 Point-Slope Form:. Linear Parent Function: is y = x or f(x) = x. Linear Equation: is an equation that models a linear function. Y-intercept: The point where the graph crosses the y-axis. GOAL:.

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5.4 Point-Slope Form:

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  1. Parent Graph: Simplest function of a family of functions with common characteristics. 5.4 Point-Slope Form: Linear Parent Function: is y = x or f(x) = x. Linear Equation: is an equation that models a linear function. Y-intercept: The point where the graph crosses the y-axis.

  2. GOAL:

  3. Whenever we are given a graph we must be able to provide the equation of the function. Point-Slope Form: The linear equation of a nonvertical line with slope m and a point (x1, y1) is: y-y1 = m(x-x1) Y value of given point. X value of given point. Slope = =

  4. Where does - = m(-) come from: Slope = Definition of Slope The variable we use for slope Slope = m Let be any point on the line and substitute () for () = m = m Isolate - =m(x) Point-Slope form.

  5. EX: Provide the equation of the line that passes through (8, -4) and has a slope of 2/3

  6. SOLUTION: Provide the equation of the line that passes through (8, -4) and has a slope of 2/3 Given: slope = point: (8, -4) m = (8, -4) = (x1, y1) =m(x) =(x) Substitute point

  7. =(x) =(x) (-)(-) = + =x Distribute slope Isolate y =x Common denominator = x

  8. Graph: = x b = -9.3 Slope up 2 right 3

  9. YOU TRY IT:Provide the equation of the line that passes through (3, 2) and has a slope of 4/9

  10. YOU TRY IT: (Solution) Provide the equation of the line that passes through (3, 2) and has a slope of 4/9 Given: slope = point: (3, 2) m = (3, 2) = (x1, y1) =m(x) =(x) Substitute point

  11. =(x) =x Distribute slope Isolate y =x Common denominator = x

  12. Graph: = x b  = = 0.66 Slope up 4 right 9

  13. CLASSWORK:Page 316-317 Problems: 2, 3, 5, 8, 11,

  14. HOW TO GRAPH POINT-SLOPE FORM: We can graph this equation by looking at the given information within the equation. EX: Graph y – 1 = (x – 2)

  15. Use the given point and slope: Graph y – 1 = (x – 2) We can see from the equation that Point (2,1) Slope m= Two up Three right.

  16. YOU TRY IT:Graph the following equation: y – 4 = - (x + 3)

  17. Use the given point and slope: y – 4 = - (x + 3) We can see from the equation that Point (-3 ,4) Opposite of what we see! Slope m=- Down one right two.

  18. CLASSWORK:Page 316-317 Problems: 12, 13, 14, 15

  19. USING TWO POINTS TO WRITE THE POINT-SLOPE FORM: Provide the point-slope equation of the line that passes through (-2, -3) and (1, 4)

  20. In order to provide the point-slope equation of the line that passes through (-2, -3) and (1, 4) we must: 1. Find the slope m =  m =  m = 2. Use one of the given points (either one) =(x) Choosing: (1, 4) =(x) Choosing: (-2, -3)

  21. YOU TRY IT: Provide the point-slope equation of the line that passes through (6, -2) and (-1, 3)

  22. In order to provide the point-slope equation of the line that passes through (6, -2) and (-1, 3) we must: 1. Find the slope m =  m =  m = - 2. Use one of the given points (either one) =-(x) Choosing: (6, -2) =- (x) Choosing: (-1, 3)

  23. CLASSWORK:Page 316-317 Problems: 19, 20, 21,

  24. WRITING THE POINT-SLOPE FORM FROM A TABLE: Provide the point-slope equation shown by the following data:

  25. Use two data points to find the rate-of-change (slope): m = m = m = Use the equation with a point, say (70, 490) =(x)

  26. YOU TRY IT: Provide the point-slope equation shown by the following data:

  27. Use two data points to find the rate-of-change (slope): m = m = m = Use the equation with a point, say (70, 490) =(x)

  28. VIDEOS: Graphs https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/point-slope-form/v/idea-behind-point-slope-form https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/point-slope-form/v/linear-equations-in-point-slope-form

  29. CLASSWORK:Page 316-317 Problems:As many as needed to master the concept

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