1. College Algebra Chapter 2 Functions and Graphs
Section 2.4
Linear Equations in Two Variables and Linear Functions
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2. Concepts Graph Linear Equations in Two Variables
Determine the Slope of a Line
Apply the Slope-Intercept Form of a Line
Compute Average Rate of Change
Solve Equations and Inequalities Graphically

3. Concept 1 Graph Linear Equations in Two Variables

4. Graph Linear Equations in Two Variables
Standard form of the equation of line: Ax + By = C where A and B are real numbers and A and B are not both zero.

5. Example 1
Graph the equation and identify the x- and y-intercepts. 3x-2y=6 Solution:

6. Example 2
Graph the equation and identify the x- and y-intercepts. 5x=-10 Solution:
x-int 5x=-10, x=-2 (-2,0) y-int none vertical line

7. Example 3 Graph the equation and identify the x- and y-intercepts. y=2
x-int none y-int y=2 (0,2) Horizontal line

8. Skill Practice 1 Graph the line represented by each equation. 4x+2y=2

9. Concept 2 Determine the Slope of a Line

10. Determine the Slope of a Line
Slope of a line through

11. Example 4
Find the slope of a line passing through the given points. (-2,3) and (1,-8)

12. Example 5
Find the slope of a line passing through the given points.

13. Skill Practice 2
Find the slope of the line passing through the given points.
(-4,1) and (2,-2)

14. Example 6
Find the slope of the horizontal line y = 4 Solution: Slope of horizontal=0 X Y 1 4 2 50

15. Example 7
Find the slope of the vertical line x = –3 Solution: Slope of vertex undefined x y -3 1 2 3

16. Skill Practice 3 Fill in the blank.
The slope of a vertical line is________.
The slope of a Horizontal line is________.

17. Determine the Slope of a Line (1 of 2)
Linear Equations and Slopes of Lines
Slanted line
Ax + By = C
(A  0, B  0)
Positive slope
Negative slope

18. Determine the Slope of a Line (2 of 2)
Horizontal line
y = k
(k is a constant)
Zero slope
Vertical line
x = k
(k is a constant)
Undefined slope

19. Concept 3 Apply the Slope-Intercept Form of a Line

20. Apply the Slope-Intercept Form of a Line
Slope-intercept form of a line: y = mx + b slope is m, y-intercept is (0, b)

21. Example 8
Write the equation in slope-intercept form. Use the slope and y-intercept to graph the line.

22. Example 9
Write the equation in slope-intercept form. Use the slope and y-intercept to graph the line.

23. Skill Practice 4 Given 2x+4y=8,
Write the equation in slope-intercept form.
Determine the slope and y-intercept.
Graph the line by using the slope and y- intercept.

24. Example 10
Write an equation of the line in slope-intercept form that passes through the point (–2, 3) and has slope 5. Solution: Y =mx + c 3 =5(-2) + b 3 =-10 + b 13 =b M=5 X=-2,y=3 m = 5 b = 13 y= 5x + 13

25. Skill Practice 5
Write an equation of the line that passes through the point (-1,-4) and has slope 3.Then write the equation using function notation.

26. Concept 4 Compute Average Rate of Change

27. Compute Average Rate of Change (1 of 2)
If f is defined on the interval
then the average rate of change of f on the interval
is the slope of the secant line containing

28. Compute Average Rate of Change (2 of 2)

29. Examples 11 – 12
Determine the average rate of change

30. Skill Practice 6 Refer to the graph in Example 6.
Determine the average rate of change of blood alcohol level from
Round to 3 decimal places.
Interpret the result from part(a)

31. Skill Practice 7 Given the function defined by
determine the average rate of change from

32. Concept 5 Solve Equations and Inequalities Graphically

33. Example 13
Use the graph to solve the equation. 0.5x + 1 = 3x – 4 Solution: From graph, x = 2 10(0.5x+1) = 10(3x-4) 5x + 10 = 30 x x = -50 X=2

34. Examples 14, 15
Use the graph to solve the inequalities.

35. Skill Practice 8
Use the graph to solve the equation and inequalities.

36. Skill Practice 9
Solve the equation 3x-(x+1)-1=0 and verify the solution graphically on a graphing utility.
Use the graph to find the solution set to the inequality
Use the graph to find the solution set to the inequality