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### 2 3 Bzca5e

1. 1. Section 2.3 Linear Functions and Slopes
2. 2. The Slope of a Line
3. 5. Example Find the slope of the line passing through the pair of points. (5,-2) and (-1,7)
4. 6. The Point-Slope Form of the Equation of a Line
5. 8. Solving in both forms <ul><li>A.Write the equation in point slope form of the line with slope 4 that passes through the point (4,-3). B.Then solve the equation for y </li></ul>y-(-3) = 4(x-4) Substituting the values into the euation y+3 = 4(x-4) This is Point Slope Form. Apply the distributive property for the parentheses. This will give us the slope intercept form. (The equation is solved for y.) -3 -3 y= 4(x-4) -3 y= 4x-16-3 <ul><li>y-y 1 = m(x-x 1 ) </li></ul>(slope intercept form) Y=4x-19 y 1 x 1
6. 9. Example Write the point slope form of the equation of the line with slope of -4 that passes through (2,5). Then solve for y.
7. 10. If you are given two points and you need to write an equation in point-slope form, then you can use either point for (x 1 ,y 1 ).
8. 12. Example Write the point slope form of the equation of the line that passes through (2,5) and (-1,0). Then solve for y.
9. 13. The Slope-Intercept Form of the Equation of a Line
10. 15. Two forms for Equations of Lines Slope Intercept Form For a nonvertical line with slope m and y-intercept b the equation is y=mx+b Example: slope =2 y-intercept of 6 Y=2x +6 Point Slope Form For a nonvertical line with slope m that passes through (x 1 ,y 1 ) the equation is y-y 1 = m(x-x 1 ) Example: slope = -3 point on the line(-1,-2) Y-(-2)= -3(x-(-1)) Y+2= -3(x+1)
11. 17. Graph the linear equation y= 2/3x+4 First: Plot the y-intercept of 4 Rise by 2 units Run ( go to the right) by 3 units. Plot the second point (3, 6) Connect the two points with a straight edge or ruler. (0,4) (3,6)
12. 18. Example Graph the linear equation y= -3x+5
13. 19. Example
14. 20. Equations of Horizontal and Vertical Lines
15. 23. Example Graph x=4. Graph y=-2
16. 24. The General Form of the Equation of a Line
17. 26. Y intercept slope
18. 27. Example Find the slope and the y intercept of the line whose equation is 2x+5y-10=0.
19. 28. Using Intercepts to Graph Ax + By + C = 0
20. 30. Find x and y intercepts to graph a line 6x-2y=12 0 0 6x-2(0)=12 6x=12 X=2 (2,0) Y=-6 (0,-6) -2y=12 6(0)-2y=12 Y intercept so let x=0 X intercept so let y=0
21. 32. Example Find the x and y intercepts then graph using those points. X-4y-8=0
22. 33. Summary
23. 34. Applications
24. 37. Example 12.80 9.60 8.00 6.40 Price 16 12 10 8 Diameter
25. 38. Graphing Calculator-Linear Regression More on the next slide. 12.8 16 9.60 12 8.00 10 6.40 8 \$ D
26. 39. Graphing Calculator-Linear Regression continued
27. 40. (a) (b) (c) (d) Find the equation of the line in slope-intercept form for a line that passes through (0,-4) and has a slope of -2.
28. 41. (a) (b) (c) (d) Find the equation of the line in slope-intercept form of the line that passes through (-3,-2) and (0,-2).
29. 42. (a) (b) (c) (d) What is the slope of the line 3x - 7y – 4 = 0.