1. Writing Linear Functions
2-4
Writing Linear Functions
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 2

2. Warm Up Write each function in slope-intercept form.
1. 4x + y = 8 2. –y = 3x 3. 2y = 10 – 6x
Determine whether each line is vertical or horizontal.
y = 0
y = –4x + 8
y = –3x
y = –3x + 5 3 4
x =
vertical
horizontal

3. Objectives
Use slope-intercept form and point-slope form to write linear functions.
Write linear functions to solve problems.

4. Vocabulary
Point-slope form

5. Recall from Lesson 2-3 that the slope-intercept form of a linear equation is
y= mx + b,
where m is the slope of the line
and b is its y-intercept.

6. Example 1: Writing the Slope-Intercept Form of the Equation of a Line
Write the equation of the graphed line in slope-intercept form.
Step 1
Identify the y-intercept.
The y-intercept b is 1.

7. Example 1 Continued Step 2 Find the slope.
Choose any two convenient points on the line, such as (0, 1) and (4, –2). Count from (0, 1) to (4, –2) to find the rise and the run. The rise is –3 units and the run is 4 units. 3 –4 4 –3
Slope is = = – .
rise
run –3 4 3

8. Example 1 Continued
Step 3
Write the equation in slope-intercept form.
y = mx + b 3 4
y = – x + 1
m = – and b = 1. 3 4
The equation of the line is 3 4
y = – x + 1.

9. Check It Out! Example 1
Write the equation of the graphed line in slope-intercept form.
Step 1
Identify the y-intercept.
The y-intercept b is 3.

10. Check It Out! Example 1 Continued
Step 2 Find the slope.
Choose any two convenient points on the line, such as (–4, 0) and (0, 3). Count from (–4, 0) to (0, 3) to find the rise and the run. The rise is 3 units and the run is 4 units 3 3 4
Slope is =
rise
run 3 4

11. Check It Out! Example 1 Continued
Step 3
Write the equation in slope-intercept form.
y = mx + b 3 4
y = x + 3
m = and b = 3. 3 4
The equation of the line is 3 4
y = x + 3.

12. Notice that for two points on a line, the rise is the differences in the y-coordinates, and the run is the differences in the x-coordinates. Using this information, we can define the slope of a line by using a formula.

13. Example 2A: Finding the Slope of a Line Given Two or More Points
Find the slope of the line through (–1, 1) and (2, –5).
Let (x1, y1) be (–1, 1) and (x2, y2) be (2, –5).
Use the slope formula.
The slope of the line is –2.

14. Example 2B: Finding the Slope of a Line Given Two or More Points
Find the slope of the line. x 4 8 12 16 y 2 5 11
Choose any two points.
Let (x1, y1) be (4, 2) and (x2, y2) be (8, 5).
Use the slope formula.
The slope of the line is . 3 4

15. Example 2C: Finding the Slope of a Line Given Two or More Points
Find the slope of the line shown.
Let (x1, y1) be (0,–2) and (x2, y2) be (1, –2).
The slope of the line is 0.

16. Because the slope of line is constant, it is possible to use any point on a line and the slope of the line to write an equation of the line in point-slope form.

17. Example 3: Writing Equations of Lines
In slope-intercept form, write the equation of the line that contains the points in the table. x –8 –4 4 8 y –5
–3.5
–0.5 1
First, find the slope. Let (x1, y1) be (–8, –5) and (x2, y2) be (8, 1).
Next, choose a point, and use either form of the equation of a line.

18. Example 3 Continued
Method A Point-Slope Form
Rewrite in slope-intercept form.
Using (8, 1):
y – y1 = m(x – x1)
Distribute.
Substitute.
Solve for y.
Simplify.

19. Example 3 Continued
Method B Slope-intercept Form
Using (8, 1), solve for b.
Rewrite the equation using m and b.
y = mx + b
y = mx + b
Substitute.
1 = 3 + b
Simplify.
b = –2
Solve for b.
The equation of the line is

20. Check It Out! Example 3a
Write the equation of the line in slope-intercept form with slope –5 through (1, 3).
Method A Point-Slope Form
y – y1 = m(x – x1)
y – (3) = –5(x – 1)
Substitute.
y – 3 = –5(x – 1)
Simplify.
Rewrite in slope-intercept form.
y – 3 = –5(x – 1)
y – 3 = –5x + 5
Distribute.
The equation of the line is y = –5x + 8.
y = –5x + 8
Solve for y.

21. Check It Out! Example 3b
Write the equation of the line in slope-intercept form through (–2, –3) and (2, 5).
First, find the slope. Let (x1, y1) be (–2,–3) and (x2, y2) be (2, 5).
Method B Slope-Intercept Form
y = mx + b
Rewrite the equation using m and b.
5 = (2)2 + b
5 = 4 + b
y = 2x + 1
y = mx + b
1 = b
The equation of the line is y = 2x + 1.

23. Example 5A: Writing Equations of Parallel and Perpendicular Lines
Write the equation of the line in slope-intercept form.
parallel to y = 1.8x + 3 and through (5, 2)
m = 1.8
Parallel lines have equal slopes.
Use y – y1 = m(x – x1) with (x1, y1) = (5, 2).
y – 2 = 1.8(x – 5)
y – 2 = 1.8x – 9
Distributive property.
y = 1.8x – 7
Simplify.

24. Example 5B: Writing Equations of Parallel and Perpendicular Lines
Write the equation of the line in slope-intercept form.
perpendicular to and through (9, –2)
The slope of the given line is , so the slope of
the perpendicular line is the opposite reciprocal, .
Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2).
Distributive property.
Simplify.

25. Lesson Quiz: Part I
Write the equation of each line in slope-intercept form. 1.
2. parallel to y = 0.5x + 2 and through (6, 1)
3. perpendicular to and through (4, 4)
y = –2x –1
y = 0.5x – 2

26. Lesson Quiz: Part II
4. Express the catering cost as a function of the number of people. Find the cost of catering a meal for 24 people.
Number in Group
Cost ($) 4 98 7
134 15
230
f(x) = 12x + 50; $338