1. 3
Chapter
Chapter 2
Graphing

2. Section
3.5
Equations of Lines

3. Using the Slope-Intercept Form to Graph an Equation
Objective 1
Using the Slope-Intercept Form to Graph an Equation

4. Slope-Intercept Form Slope-Intercept Form of a line
When a linear equation in two variables is written in slope-intercept form,
y = mx + b
then m is the slope of the line and (0, b) is the y-intercept of the line.
slope (0, b), y-intercept

5. Example Use the slope-intercept form to graph the equation.
The slope is 3/5.
The y-intercept is –2.
Begin by graphing (0, –2),
move up 3 units and right 5 units.

6. Using the Slope-Intercept Form to Write an Equation
Objective 2
Using the Slope-Intercept Form to Write an Equation

7. Example
Find an equation of the line with y-intercept (0, –2) and slope 3/5.

8. Writing an Equation Given Slope and a Point
Objective 3
Writing an Equation Given Slope and a Point

9. Point-Slope Form The point-slope form of the equation of a line is
where m is the slope of the line and (x1, y1) is a point on the line.

10. Example y + 12 = –2x – 22 Use the distributive property.
Find an equation of the line with slope –2 that passes through (–11, –12). Write the equation in slope-intercept form, y = mx + b, and in standard form, Ax + By = C.
We substitute the slope and point into the point-slope form of an equation.
y – (–12) = – 2(x – (– 11))
Let m = –2 and (x1, y1) = (–11, –12).
y + 12 = –2x – 22 Use the distributive property.
y = –2x – 34 Slope-intercept form.
2x + y = – Add 2x to both sides and we have standard form.

11. Writing an Equation Given Two Points
Objective 4
Writing an Equation Given Two Points

12. Example
Find an equation of the line through (–4, 0) and (6, –1). Write the equation in standard form.
First, find the slope.
Continued

13. Example (cont)
Now substitute the slope and one of the points into the point-slope form of an equation.
10y = –1(x + 4)
Clear fractions by multiplying both sides by 10.
10y = –x – 4
Use the distributive property.
x + 10y = –4
Add x to both sides.

14. Finding Equations of Vertical and Horizontal Lines
Objective 5
Finding Equations of Vertical and Horizontal Lines

15. Example
Find an equation of the vertical line through (–7, –2). The equation of a vertical line can be written in the form x = c, so an equation for a vertical line passing through (–7, –2) is x = –7.

16. Example
Find an equation of the line parallel to the line y = –3 and passing through (10, 4). Since the graph of y = –3 is a horizontal line, any line parallel to it is also horizontal. The equation of a horizontal line can be written in the form y = c. An equation for the horizontal line passing through (10, 4) is y = 4.

17. Using the Point-Slope Form to Solve Problems
Objective 6
Using the Point-Slope Form to Solve Problems

18. Example
In 1997, Window World , Inc. had 50 employees. In 2012, the company had 85 employees. Let x represent the number of years after 1997 and let y represent the number of employees.
a.) Assume that the relationship between years and number of employees is linear, write an equation describing this relationship.
b.) Use the equation to predict the number of employees in 2007.
Continued

19. Example (cont) Continued
a. The year 1997 is represented by x = is 15 year after 1997, so 2012 is represented by x = 15. The two points (0, 50) and (15, 85) will be used to find the equation.
Substitute the values for m, x1, and y1.
Distribute.
Add 50 to both sides.
Continued

20. Example (cont) Use the equation to predict the number
of employees in 2007.
In 2007, x = 10.