splash screen. lesson menu five-minute check (over lesson 3–3) then/now new vocabulary key...
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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
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A.
B.
C.
D.
What is the slope of the line MN for M(–3, 4) and N(5, –8)?
Over Lesson3–3
A. A
B. B
C. C
D. D A B C D
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A.
B.
C.
D.
What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?
Over Lesson3–3
A. A
B. B
C. C
D. D A B C D
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A.
B.
C.
D.
What is the slope of a line parallel to MN forM(–3, 4) and N(5, –8)?
Over Lesson3–3
A. B.
C. D.
A. A
B. B
C. C
D. D A B C D
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What is the graph of the line that has slope 4 and contains the point (1, 2)?
Over Lesson3–3
A. A
B. B
C. C
D. D A B C D
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What is the graph of the line that has slope 0 and contains the point (–3, –4)?
A. B.
C. D.
Over Lesson3–3
A. A
B. B
C. C
D. D A B C D
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A. (–2, 2)
B. (–1, 3)
C. (3, 3)
D. (4, 2)
You found the slopes of lines. (Lesson 3–3)
• Write an equation of a line given information about the graph.
• 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
Answer: Plot a point at the y-intercept, –3.
Use the slope of 6 or to find
another point 6 units up and1 unit right of the y-intercept.
Draw a line through these two points.
A. A
B. B
C. C
D. D A B C D
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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.
Slope and a Point on the Line
Point-slope form
Write an equation in point-slope form of the line
whose slope is that contains (–10, 8). Then
graph the line.
Simplify.
Slope and a Point on the Line
Answer: 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.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Write an equation in point-slope form of the line
whose slope is that contains (6, –3).
A.
B.
C.
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.
Distributive Property
Add 9 to each side.
Answer:
Point-slope form
Using (4, 9):
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.
Distributive Property
Answer:
m = 5, (x1, y1) = (–1, 3)
Point-slope form
Using (–1, 3):
Add 3 to each side.y = 5x + 8
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8).
A.
B.
C.
D.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
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).
Horizontal Line
Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form.
Slope formula
This is a horizontal line.
Step 1
Horizontal Line
Point-Slope form
m = 0, (x1, y1) = (5, –2)
Step 2
Answer:
Simplify.
Subtract 2 from each side.y = –2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Write an equation of the line through (–4, –8) and (–1, –6) in slope-intercept form.
A.
B.
C.
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
C. y = –3x + 8
D.
A. A
B. B
C. C
D. D A B C D
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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.
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
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?
Write Linear Equations
Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.
A. A
B. B
C. C
D. D A B C D
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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. A
B. B
C. C
D. D A B C D
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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?
