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Five-Minute Check (over Lesson 3–3)
CCSS
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 Equations of Parallel or Perpendicular Lines
Example 6: Real-World Example: Write Linear Equations
Over Lesson 3–3
What is the slope of the line MN for M(–3, 4) and
N(5, –8)?
A.
B.
C.
D.
Over Lesson 3–3
What is the slope of the line MN for M(–3, 4) and
N(5, –8)?
A.
B.
C.
D.
Over Lesson 3–3
What is the slope of a line perpendicular to MN for
M(–3, 4) and N(5, –8)?
A.
B.
C.
D.
Over Lesson 3–3
What is the slope of a line perpendicular to MN for
M(–3, 4) and N(5, –8)?
A.
B.
C.
D.
Over Lesson 3–3
What is the slope of a line parallel to MN for
M(–3, 4) and N(5, –8)?
A.
B.
C.
D.
Over Lesson 3–3
What is the slope of a line parallel to MN for
M(–3, 4) and N(5, –8)?
A.
B.
C.
D.
Over Lesson 3–3
What is the graph of the line that has slope 4 and
contains the point (1, 2)?
A.
B.
C.
D.
Over Lesson 3–3
What is the graph of the line that has slope 4 and
contains the point (1, 2)?
A.
B.
C.
D.
Over Lesson 3–3
What is the graph of the line that has slope 0 and
contains the point (–3, –4)?
A.
B.
C.
D.
Over Lesson 3–3
What is the graph of the line that has slope 0 and
contains the point (–3, –4)?
A.
B.
C.
D.
Over Lesson 3–3
A. (–2, 2)
B. (–1, 3)
C. (3, 3)
D. (4, 2)
Over Lesson 3–3
A. (–2, 2)
B. (–1, 3)
C. (3, 3)
D. (4, 2)
Content Standards
G.GPE.5 Prove the slope criteria for parallel and
perpendicular lines and use them to solve
geometric problems (e.g., find the equation of a
line parallel or perpendicular to a given line that
passes through a given point).
Mathematical Practices
4 Model with mathematics.
8 Look for and express regularity in repeated
reasoning.
You found the slopes of lines.
• Write an equation of a line given information
about the graph.
• Solve problems by writing equations.
• slope-intercept form
• point-slope form
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
Answer:
Plot a point at the
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.
Slope and y-intercept
Answer:
Plot a point at the
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
C. y = –x – 4
D. y = –x + 4
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
C. y = –x – 4
D. y = –x + 4
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
Graph the given point
(–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.
Answer:
Slope and a Point on the Line
Graph the given point
(–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.
Answer:
Write an equation in point-slope form of the line
whose slope is
A.
B.
C.
D.
that contains (6, –3).
Write an equation in point-slope form of the line
whose slope is
A.
B.
C.
D.
that contains (6, –3).
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
Add 9 to each side.
Answer:
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
Add 9 to each side.
Answer:
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
Answer:
Add 3 to each side.
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
Answer:
Add 3 to each side.
A. Write an equation in slope-intercept form for a
line containing (3, 2) and (6, 8).
A.
B.
C.
D.
A. Write an equation in slope-intercept form for a
line containing (3, 2) and (6, 8).
A.
B.
C.
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
C. y = 3x – 2
D. y = 3x + 1
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
C. y = 3x – 2
D. y = 3x + 1
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
Answer:
Subtract 2 from each side.
Horizontal Line
Step 2
Point-Slope form
m = 0, (x1, y1) = (5, –2)
Simplify.
y = –2
Answer:
Subtract 2 from each side.
Write an equation of the line through (–3, 6) and
(9, –2) in slope-intercept form.
A.
B.
C.
D.
Write an equation of the line through (–3, 6) and
(9, –2) in slope-intercept form.
A.
B.
C.
D.
Write Equations of Parallel or Perpendicular Lines
y = mx + b
Slope-Intercept form
0 = –5(2) + b
m = –5, (x, y) = (2, 0)
0 = –10 + b
Simplify.
10 = b
Answer:
Add 10 to each side.
Write Equations of Parallel or Perpendicular 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
C. y = –3x + 8
D.
A. y = 3x
B. y = 3x + 8
C. y = –3x + 8
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:
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:
A = 525r + 750
= 525(12) + 750
= 7050
Second complex:
A = 600r + 200
r = 12
= 600(12) + 200
Simplify.
= 7400
Write Linear Equations
Answer:
Write Linear Equations
Answer: The first complex offers the better rate: one
year costs $7050 instead of $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
C. C = 100d + 25
D. C = 25d + 100
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
C. C = 100d + 25
D. C = 25d + 100
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
B. second company
C. neither
D. cannot be determined
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
B. second company
C. neither
D. cannot be determined