# Glencoe Geometry

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```					Five-Minute Check (over Lesson 3–3)
Then/Now
New Vocabulary
Key Concept: Nonvertical Line Equations
Example 1: Slope and y-intercept
Example 2: Slope and a Point on the Line
Example 3: Two Points
Example 4: Horizontal Line
Key Concept: Horizontal and Vertical Line Equations
Example 5: Write Parallel or Perpendicular Equations of Lines
Example 6: Real-World Example: Write Linear Equations
Over Lesson3–3

What is the slope of the line MN for M(–3, 4) and
N(5, –8)?

A.

B.                                           A.     A
B.     B
C.
C.     C
D.                                           D.     D
Over Lesson3–3

What is the slope of a line perpendicular to MN for
M(–3, 4) and N(5, –8)?

A.

B.                                           A.   A
B.   B
C.
C.   C
D.
D.   D
Over Lesson3–3

What is the slope of a line parallel to MN for
M(–3, 4) and N(5, –8)?

A.

B.                                               A.   A
B.   B
C.
C.   C
D.                                               D.   D
Over Lesson3–3

What is the graph of the line that has slope 4 and
contains the point (1, 2)?
A.             B.

A.   A
B.   B
C.             D.
C.   C
D.   D
Over Lesson3–3

What is the graph of the line that has slope 0 and
contains the point (–3, –4)?
A.              B.

A.   A
B.   B
C.              D.
C.   C
D.   D
Over Lesson3–3

A. (–2, 2)
A.   A
B. (–1, 3)                    B.   B
C. (3, 3)                     C.   C
D.   D
D. (4, 2)
You found the slopes of lines. (Lesson 3–3)

• Write an equation of a line given information
• Solve problems by writing equations.
Slope and y-intercept

Write an equation in slope-intercept form of the line
with slope of 6 and y-intercept of –3. Then graph the
line.

y = mx + b           Slope-intercept form

y = 6x + (–3)        m = 6, b = –3

y = 6x – 3           Simplify.
Slope and y-intercept

Plot a point at the                   Answer:
y-intercept, –3.

Use the slope of 6 or      to find

another point 6 units up and
1 unit right of the y-intercept.

Draw a line through these two
points.
Write an equation in slope-intercept form of the line
with slope of –1 and y-intercept of 4.

A. x + y = 4

B. y = x – 4
A.   A
C. y = –x – 4                                  B.   B
C.   C
D. y = –x + 4
D.   D
Slope and a Point on the Line

Write an equation in point-slope form of the line
whose slope is       that contains (–10, 8). Then
graph the line.

Point-slope form

Simplify.
Slope and a Point on the Line

(–10, 8).

Use the slope

to find another point 3 units
down and 5 units to the right.

Draw a line through these
two points.
Write an equation in point-slope form of the line
whose slope is    that contains (6, –3).

A.

B.                                            A.    A
B.    B
C.                                            C.    C
D.    D
D.
Two Points

A. Write an equation in slope-intercept form for a
line containing (4, 9) and (–2, 0).
Step 1 First find the slope of the line.

Slope formula

x1 = 4, x2 = –2, y1 = 9, y2 = 0

Simplify.
Two Points

Step 2 Now use the point-slope form and either point
to write an equation.
Using (4, 9):
Point-slope form

Distributive Property

Two Points

B. Write an equation in slope-intercept form for a
line containing (–3, –7) and (–1, 3).
Step 1 First find the slope of the line.

Slope formula

x1 = –3, x2 = –1, y1 = –7, y2 = 3

Simplify.
Two Points

Step 2 Now use the point-slope form and either point
to write an equation.
Using (–1, 3):
Point-slope form

m = 5, (x1, y1) = (–1, 3)

Distributive Property

y = 5x + 8           Add 3 to each side.

A. Write an equation in slope-intercept form for a
line containing (3, 2) and (6, 8).

A.

B.
A.    A
C.                                             B.    B
C.    C
D.                                             D.    D
B. Write an equation in slope-intercept form for a
line containing (1, 1) and (4, 10).

A. y = 2x – 3

B. y = 2x + 1
A.    A
C. y = 3x – 2                                  B.    B
C.    C
D. y = 3x + 1
D.    D
Horizontal Line

Write an equation of the line through (5, –2) and
(0, –2) in slope-intercept form.
Step 1

Slope formula

This is a horizontal line.
Horizontal Line

Step 2

Point-Slope form

m = 0, (x1, y1) = (5, –2)

Simplify.

y = –2                 Subtract 2 from each side.

Write an equation of the line through (–4, –8) and
(–1, –6) in slope-intercept form.

A.

B.
A.    A
C.                                             B.    B
C.    C
D.                                             D.    D
Write Parallel or Perpendicular Equations of Lines

y = mx + b              Slope-Intercept form
0 = –5(2) + b           m = 5, (x, y) = (2, 0)
0 = –10 + b             Simplify.
10 = b                   Add 10 to each side.
Answer: So, the equation is y = 5x + 10.
A. y = 3x

B. y = 3x + 8    A.   A
B.   B
C. y = –3x + 8
C.   C
D.               D.   D
Write Linear Equations

RENTAL COSTS An apartment complex charges
\$525 per month plus a \$750 annual maintenance fee.
A. Write an equation to represent the total first
year’s cost A for r months of rent.
For each month of rent, the cost increases by \$525. So
the rate of change, or slope, is 525. The y-intercept is
located where 0 months are rented, or \$750.
A = mr + b           Slope-intercept form
A = 525r + 750       m = 525, b = 750
Answer: The total annual cost can be represented by
the equation A = 525r + 750.
Write Linear Equations

RENTAL COSTS An apartment complex charges
\$525 per month plus a \$750 annual maintenance fee.
B. Compare this rental cost to a complex which
charges a \$200 annual maintenance fee but \$600 per
month for rent. If a person expects to stay in an
apartment for one year, which complex offers the
better rate?
Evaluate each equation for r = 12.
First complex:                  Second complex:
A = 525r + 750                  A = 600r + 200
= 525(12) + 750    r = 12       = 600(12) + 200
= 7050             Simplify.    = 7400
RENTAL COSTS A car rental company charges
\$25 per day plus a \$100 deposit.
A. Write an equation to represent the total cost C
for d days of use.
A. C = 25 + d + 100

B. C = 125d
A.     A
B.     B
C. C = 100d + 25
C.     C
D. C = 25d + 100                              D.     D
RENTAL COSTS A car rental company charges
\$25 per day plus a \$100 deposit.
B. Compare this rental cost to a company which
charges a \$50 deposit but \$35 per day for use. If a
person expects to rent a car for 9 days, which
company offers the better rate?
A. first company                              A.   A
B. second company
B.   B
C.   C
C. neither
D.   D
D. cannot be determined
• Homework p 200 13, 17, 20, 21, 29, 30,
37, 40

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