1. 5.4 Point-Slope Form: Linear Parent Function: is y = x or f(x) = x. Parent Graph: Simplest function of a family of functions with common characteristics. 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 (x 1, y 1 ) is: y-y 1 = m(x - x 1 ) X value of given point. Y value of given point.

4. Slope = m Definition of Slope The variable we use for slope 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 Substitute point

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

8. Graph:

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 Substitute point

11. Distribute slope Isolate y Common denominator

12. Graph:

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.

15. Use the given point and slope: We can see from the equation that Point  (2,1)

16. YOU TRY IT: Graph the following equation:

17. Use the given point and slope: We can see from the equation that Point  (-3,4)  Opposite of what we see!

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 2. Use one of the given points (either one) Choosing: (1, 4) 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 2. Use one of the given points (either one) Choosing: (6, -2) 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: Time, X (s) Attitude, y (m) 10640 30590 70490 90440

25. Use two data points to find the rate-of- change (slope): Time, X (s) Attitude, y (m) 10640 30590 70490 90440 Use the equation with a point, say (70, 490)

26. YOU TRY IT: Provide the point-slope equation shown by the following data: Time, X (h) Water, y (gal) 23320 34570 57070 810,820

27. Use two data points to find the rate-of- change (slope): Use the equation with a point, say (70, 490) Time, X (h) Water, y (gal) 23320 34570 57070 810,820

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

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