1. Section 2.2
Linear Equations

2. Graphing Linear Equations
Definition 1: A function whose graph is a line is a linear function.
Definition 2: You can represent a linear function with a linear equation.
Definition 3: Because the value of y depends on the value of x, y is called the dependent variable and x is called the independent variable.

3. Examples 1 – 2
Graph each equation.
y = 2/3x + 3
y = 3/4x

4. Examples 3 – 4
Graph each equation.
x + y = -2
y = -1/2x + 1/2

5. Graphing Linear Equations
Definition 4: The y-intercept of a line is the point at which the line crosses the y-axis.
Definition 5: The x-intercept of a line is the point at which the line crosses the x-axis.
Definition 6: The standard form of an equation is Ax + By = C.

6. Example 5
Transportation: The equation 3x + 2y = 120 models the number of passengers who sit in a train car, where x is the number of adults and y is the number of children. Graph the equation. Explain what the x- and y-intercepts represent. Describe the domain and the range.

7. Example 5 Continued
Suppose the train system buys new train cars with molded plastic seats. The model changes to x + y = 40. Graph the equation and interpret the x- and y-intercepts.

8. TOTD
The school glee club needs a total of $4500 for a trip to Omaha, Nebraska. To make money, members are selling baseball caps for $4.50 and sweatshirts for $12.50.
Construct and equation and graph the equation, where x is the number of baseball caps and y is the number of sweatshirts sold.
Explain the meaning of the x- and y-intercepts in terms of fund-raising.

9. Slope
Definition 7: The slope of a nonvertical line is the ratio of the vertical change to a corresponding horizontal change.

10. Examples of Slopes

11. Examples 6 – 8 Find the slope of the line through each pair of points.
(3, 2) and (-9, 6)
(-2, -2) and (4, 2)
(0, -3) and (7, -9)

12. Writing Equations of Lines
Definition 8: When you know the slope and a point on a line, you can use the point-slope form to write the equation of a line.

13. Examples 9 – 10
Write in slope-intercept form the equation of each line.
m = -1/2; point: (8, -1)
slope 2; through (4, -2)

14. Example 11 Write in slope-intercept form the equation of each line.
slope 5/6; through (5, 6)

15. TOTD Find the slope of the line through each pair of points.
(1, 6) and (8, -1)
Write the equation of the line. Graph.
slope = 3; (1, 5)

16. Examples 12 – 13
Write in slope-intercept form the equation of the line through each pair of point.
(1, 5) and (4, -1)
(5, 0) and (-3, 2)

17. Examples 14 – 15
Write in slope-intercept form the equation of the line through each pair of point.
(-2, -1) and (-10, 17)
(5, 1) and (-4, -3)

18. Writing Equations of Lines
Definition 9: Another form of the equation of a line is slope-intercept form, which you can use to find the slope by examining the equation.

19. Examples 16 – 19 Find the slope of each line. 4x + 3y = 7 3x + 2y = 1
Ax + By = C

20. Summary: Equations of a line

21. TOTD
Write in point-slope form the equation of the line through each pair of points.
(-10, 3) and (-2, -5)

22. An Assortment of Lines
Horizontal Line
Vertical Line

23. An Assortment of Lines
Perpendicular Lines
Parallel Lines

24. Examples 20 – 21 Find the given lines.
Find the equation of a line that is perpendicular to y = 3/4x + 2 and passes through the point (0,4).
Find the equation that goes through the point (-1, 3) and is perpendicular to the line y = 5x – 3.

25. Examples 22 – 23 Find the given lines.
Find the equation of a line that is parallel to y = 2/3x + 5/8 and passes through the point (2,1).
Find the equation that is vertical and passes through the point (5, -3)

26. TOTD Write an equation for each line. Then graph the line.
Through (-2, 1) and parallel to y = -3x + 1