1. Section 3.2 Special Forms of Linear Equations in Two Variables

2. 3.2 Lecture Guide: Special Forms of Linear Equations in Two Variables Objective: Use the slope-intercept and point-slope forms of a linear equation.

3. Slope-Intercept Form Algebraically is the equation of a line with slope m and y-intercept. Algebraic Example Verbal Example This line has slope and a y-intercept of. Graphical Example

4. 1. The linehas a slope of ____________ and a y-intercept of ____________. 2. Graph the line using the slope and the y-intercept.

5. 3. Complete the following table. This example stresses the fact that if we know the slope and the y-intercept, then we can immediately write the equation. Also, if we have the equation in slope-intercept form, we can immediately sketch the graph because we can quickly determine the slope and the y-intercept. Slopey-interceptEquation

6. Point-Slope Form Algebraically is the equation of a line through with slope m. Algebraic Example Graphical Example Verbal Example This line passes through the point with slope.

7. 4. Complete the following table. This example stresses the fact that the point-slope form of a line is useful when the slope and a point other than the y-intercept is given. SlopePointPoint-Slope Equation

8. General Form: The general form,, of an equation is useful for writing linear equations without fractions. Write each equation in general form. 5.

9. Write each equation in general form. 6.

10. Write each equation in slope-intercept form: 7.

11. Write each equation in slope-intercept form: 8.

12. Parallel and Perpendicular Lines: Recall that parallel lines have the same slope and that perpendicular lines have slopes that are opposite reciprocals. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. 9. and

13. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. 10. and

14. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. 11. and

15. Objective: Use the special forms of equations for horizontal and vertical lines.

16. Horizontal and Vertical Lines Algebraically is the equation. Example: Numerical Example Graphical Example of a horizontal line with y-intercept Verbally This horizontal line has a y-intercept of and a slope of 0.

17. Horizontal and Vertical Lines Algebraically is the equation. Example: Numerical Example Graphical Example of a vertical line with x-intercept Verbally This vertical line has an x-intercept of and its slope is undefined.

18. 12. All points on a horizontal line have the same _____- coordinate. This is the reason that the equation of a horizontal line is of the form _________________________. The slope of a horizontal line is _____. 13. All points on a vertical line have the same _____- coordinate. This is the reason that the equation of a vertical line is of the form _________________________. The slope of a vertical line is _________________________.

19. Graph each equation by completing a table of values and then give any intercepts. Can you check both of these on a graphing calculator? If not, why not?

20. Equation:14. x-intercept: ______ y-intercept: ______ Slope: _______ Graph:

21. Equation:15. x-intercept: ______ y-intercept: ______ Slope: _______ Graph:

22. Objective: Graph a line given one point and its slope. To graph a line or to give the equation of the line, it is sufficient to know any point on the line and the slope of the line. This is equivalent to knowing any two points on the line because we can calculate the slope given any two points on the line.

23. Complete the missing information. On all graphs, clearly label at least two points. 16. Equation: Through: Slope: Graph:

24. Complete the missing information. On all graphs, clearly label at least two points. 17. Equation: Through: Slope: Graph:

25. Complete the following table. On all graphs, clearly label at least two points. 18. Equation: Through: Slope: Graph:

26. Complete the following table. On all graphs, clearly label at least two points. 19. Equation: Through: Slope: Undefined Graph:

27. Complete the following table. On all graphs, clearly label at least two points. 20. Equation: Through: Slope: Graph:

28. Complete the missing information. On all graphs, clearly label at least two points. 21. Equation: Through: Slope: Graph:

29. Write each equation in slope-intercept form. 22.

30. Write each equation in slope-intercept form. 23.

31. Use the point-slope form to write the equation passing through the given point with specified slope. Write the answer in slope-intercept form. 24.,

32. Use the point-slope form to write the equation passing through the given point with specified slope. Write the answer in slope-intercept form. 25.,

33. 26. Write in slope-intercept form the equation of a line passing through and.

34. 27. Write in slope-intercept form the equation of a line passing through and.

35. 28. Write in slope-intercept form the equation of a line passing through and parallel to.

36. 29. Write in slope-intercept form the equation of a line passing through and perpendicular to.

37. Complete the missing information. 30. Graph: Through: Slope: Equation:

38. Complete the missing information. 31. Graph: Through: Slope: Equation:

39. Complete the missing information. 32. Graph: Through: Slope: Equation:

40. Complete the missing information. 33. Graph: Through: Slope: Equation:

41. Complete the missing information. 34. Graph: Through: Slope: Point-Slope Equation: Slope-Intercept Equation:

42. Complete the missing information. 35. Graph: Through: Slope: Point-Slope Equation: Slope-Intercept Equation:

43. 36. The given table displays the dollar cost of a collect phone call based on the length of the call in minutes. (a) Determine the linear equation for the line that contains these data points. (b) Determine the meaning of m and b in this application.

44. 37. The given graph displays the dollar cost of having a clothes dryer repaired by a service shop. (a) Determine the linear equation for this line. (b) Determine the meaning of m and b in this application. Hours Cost ($)