1. College Algebra Chapter 2 Functions and Graphs
Section 2.4
Linear Equations in Two Variables and Linear Functions

2. 1. Graph Linear Equations in Two Variables
2. Determine the Slope of a Line
3. Apply the Slope-Intercept Form of a Line
4. Compute Average Rate of Change
5. Solve Equations and Inequalities Graphically

3. 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.

4. Example 1:
Graph the equation and identify the x- and y-intercepts.

5. Example 2:
Graph the equation and identify the x- and y-intercepts.

6. Example 3:
Graph the equation and identify the x- and y-intercepts.

7. 1. Graph Linear Equations in Two Variables
2. Determine the Slope of a Line
3. Apply the Slope-Intercept Form of a Line
4. Compute Average Rate of Change
5. Solve Equations and Inequalities Graphically

8. Determine the Slope of a Line
Slope of a line through and :

9. Example 4:
Find the slope of a line passing through the given points.

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

11. Example 6:
Find the slope of the horizontal line y = 4

12. Example 7:
Find the slope of the vertical line x = –3

13. Determine the Slope of a Line
Linear Equations and Slopes of Lines
Ax + By = C
(A  0, B  0)
Slanted line
y = k
(k is a constant)
Horizontal line
x = k
Vertical line
Positive
slope
Negative
Zero
Undefined slope

14. 1. Graph Linear Equations in Two Variables
2. Determine the Slope of a Line
3. Apply the Slope-Intercept Form of a Line
4. Compute Average Rate of Change
5. Solve Equations and Inequalities Graphically

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

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

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

18. Example 10:
Write an equation of the line in slope-intercept form that passes through the point (–2, 3) and has slope 5.

19. 1. Graph Linear Equations in Two Variables
2. Determine the Slope of a Line
3. Apply the Slope-Intercept Form of a Line
4. Compute Average Rate of Change
5. Solve Equations and Inequalities Graphically

20. Compute Average Rate of Change
If f is defined on the interval [x1, x2], then the average rate of change of f on the interval [x1, x2] is the slope of the secant line containing (x1, f(x1)) and (x2, f(x2)).
Average rate of change: or

21. Examples 11 – 12:
Determine the average rate of change
From (–1.5, 0) to (0, 2)
From (0, 2) to ( 2.5, 1)

22. 1. Graph Linear Equations in Two Variables
2. Determine the Slope of a Line
3. Apply the Slope-Intercept Form of a Line
4. Compute Average Rate of Change
5. Solve Equations and Inequalities Graphically

23. Example 13:
Use the graph to solve the equation.

24. Examples 14, 15:
Use the graph to solve the inequalities.