Beginning Algebra Lesson 11 – Linear Functions, Part 2

Writing the Equation of a Line

in Slope-Intercept Form

Slope-Intercept Form y = mx + b

Example 1: Give the equation of the line in slope-intercept form

a. With y-intercept (0, 2) and slope -9

b. Passing through (2, 3) with slope -5

c. Passing through (2, 6) and (4, 16)

Example 2: Give the equation of the linear function that would generate the following table

of values. Use your calculator to check.

x f (x)

-5 238

-3 174

-1 110

1 46

7 -146

12 -306

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Example 3: Give the equation of the linear function shown below.

Example 4: Give the equation of the horizontal line passing through the point (1,3).

Example 5: Give the equation of the vertical line passing through the point (1,3).

You Try

1. Give the equation of the line passing through the points (1, 7) and (3, -9).

2. Give the equation of the horizontal line passing through the point (5, 11).

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Parallel and Perpendicular Lines

Parallel Lines

The slopes of Parallel Lines are ______________________________________________

Example 1: Give the equation of the line passing through the point (8, 3) that is parallel to

the line y = –2x + 3.

Perpendicular Lines

The slopes of perpendicular lines are __________________________________________

If Line 1 and Line 2 are perpendicular to each other, then

Slope of line 1 Slope of line 2

5

–8

Example 2: Give the equation of the line passing through the point (8, 3) that is

perpendicular to the line y = –2x + 3.

Beginning Algebra Lesson 11 – Linear Functions, Part 2

You Try

3. Give the equation of the line passing through the point (–3, 1) that is parallel to the line

y = 8x – 5 .

4. Give the equation of the line passing through the point (–3, 1) that is perpendicular to the

line y = 8x – 5 .

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Applications – Slope-Intercept Form

Example 1: You have just bought a new television set for $1,400. The value of the television

set decreases by $250 per year. Write a formula which represents the value, V, of your television

as a function of its age, t, in years. Interpret the slope and intercepts.

Example 2: The height of a tree is a function of the amount of time that has passed since it was

planted. A tree was 7 feet tall 6 years after it was planted. It was 10 feet tall 15 years after it

was planted. Determine a linear function to represent this situation. Interpret the slope and

vertical intercept.

Beginning Algebra Lesson 11 – Linear Functions, Part 2

YOU TRY

5. A new Chevrolet Corvette costs $56,980. The car’s value depreciates to $31,870 after four

years.

a. Determine a linear equation to represent this situation. Clearly indicate what each

variable represents.

b. Identify the slope and explain its meaning.

c. Identify the vertical intercept, and explain its meaning.

d. Determine the horizontal intercept, and explain its meaning.

Beginning Algebra Lesson 11 – Linear Functions, Part 2

General Form: ax + by = c

Example 1: Consider the linear equation 3x – 5y = 30

a. Write this equation in slope-intercept form

b. Identify the slope

c. Determine the vertical intercept

d. Determine the horizontal intercept.

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Example 2: Draw an accurate graph of the function 3x + 2y = 16.

Slope-Intercept Form:

_______________________

Slope: ___________

Vertical Intercept: ___________

Horizontal Intercept: _________

Two additional points on the line:

___________ __________

YOU TRY

6. Draw an accurate graph of the function 4x – y = 7

Slope-Intercept Form:

_______________________

Slope: ___________

Vertical Intercept: __________

Horizontal Intercept: ________

Two additional points line:

___________ ____________

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Applications – General Form

Example 1: Tickets to the circus cost $9 for children and $15 for adults. A total of $5628

was collected in ticket sales on opening night. Let C represent the number of children attending

the circus, and let A represent the number of adults attending the circus.

a. Write an equation representing the total amount of money collected.

b. On opening night, 312 children attended the circus. How many adults were there?

YOU TRY

7. Tickets to a college play cost $4 for students and $6 for nonstudents. $2700 was collected at

the door in ticket sales. Let S represent the number of student tickets sold, and let N

represent the number of nonstudent tickets sold.

a. Write an equation representing the total amount of money collected.

b. If 342 students attended the play, how many nonstudents were there?

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Linear Inequalities in Two Variables

The Solution Set

Example 1: Graph the equation y = 2x – 3

Example 2: Which of the ordered pairs below satisfy the equation 2 3y x ?

(5, 3) (2, 1) (0, 0)

Example 3: Which of the ordered pairs below satisfy the inequality 2 3y x ?

(5, 3) (2, 1) (0, 0)

Example 4: Graph the linear inequality 2 3y x .

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Example 5: Which of the ordered pairs below satisfy the inequality? 2 3y x

(5, 3) (2, 1) (0, 0)

Example 6: Graph the linear inequality 2 3y x .

You Try

8. Which of the ordered pairs below satisfy the linear inequality y ≥ 4 – 2x?

(1,2) (0, 0) (5, 0)

9. Which of the ordered pairs below satisfy the linear inequality y < 4 – 2x?

(1,2) (0, 0) (5, 0)

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Graphing Linear Inequalities in Two Variables

Graphing The Solution Set of a Linear Inequality in Two Variables

Step 1: Rewrite the inequality as an equality statement.

Step 2: Graph the linear equation.

Step 3: Determine if the line should be solid or dotted.

If the original inequality statement is either < or >, draw a dotted line.

If the original inequality statement is either ≤ or ≥, draw a solid line.

Step 4: Choose a test point and plug it into the original inequality.

If the test point satisfies the inequality, shade in the direction of the test point.

If the test point does not satisfy the inequality, shade in the opposite direction of

the test point.

Example 1: Graph the inequality y < 5 – 3x

Example 2: Graph the inequality 3x – 2y ≥ 6

Beginning Algebra Lesson 11 – Linear Functions, Part 2

Example 3: Graph the inequality y ≥ 2x

You Try

10. Graph the inequality y > 2x – 1