1. Section 2.3 Linear Functions and Slopes

2. The Slope of a Line

5. Example
Find the slope of the line passing through the pair of points. (5,-2) and (-1,7)

6. The Point-Slope Form of the Equation of a Line

8. Solving in both forms
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 x1 y1
(slope intercept form)
y-y1 = m(x-x1)
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
Y=4x-19

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.

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 (x1,y1).

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.

13. The Slope-Intercept Form of the Equation of a Line

15. Two forms for Equations of Lines Point Slope Form Slope Intercept Form
For a nonvertical line with slope m that passes through (x1,y1) the equation is
y-y1 = m(x-x1)
Example: slope = -3
point on the line(-1,-2)
Y-(-2)= -3(x-(-1))
Y+2= -3(x+1)
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

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.
(3,6)
(0,4)

18. Example
Graph the linear equation y= -3x+5

19. Example

20. Equations of Horizontal and Vertical Lines

23. Example
Graph x=4. Graph y=-2

24. The General Form of the Equation of a Line

26. Y intercept
slope

27. Example
Find the slope and the y intercept of the line whose equation is 2x+5y-10=0.

28. Using Intercepts to Graph Ax + By + C = 0

30. Find x and y intercepts to graph a line 6x-2y=12
X intercept so let y=0
Y intercept so let x=0
6x-2(0)=12
6(0)-2y=12
6x=12
-2y=12
X=2
Y=-6
(2,0)
(0,-6)

32. Example
Find the x and y intercepts then graph using those points.
X-4y-8=0

33. Summary

34. Applications

37. Example
Diameter 8 10 12 16
Price
6.40
8.00
9.60
12.80

38. Graphing Calculator-Linear RegressionD $ 8
6.40 10
8.00 12
9.60 16
12.8
More on the next slide.

39. Graphing Calculator-Linear Regression continued

40. Find the equation of the line in slope-intercept form for a line that passes through (0,-4) and has a slope of -2.
(a)
(b)
(c)
(d)

41. Find the equation of the line in slope-intercept form of the line that passes through (-3,-2) and (0,-2).
(a)
(b)
(c)
(d)

42. What is the slope of the line 3x - 7y – 4 = 0.
(b)
(c)
(d)