geometry warm ups what is the slope of the line mn for m(–3, 4) and n(5, –8)? what is the slope...
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![Page 1: Geometry Warm ups What is the slope of the line MN for M(–3, 4) and N(5, –8)? What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?](https://reader036.vdocument.in/reader036/viewer/2022062518/56649da25503460f94a8ee18/html5/thumbnails/1.jpg)
Geometry Warm ups
What is the slope of the line MN for M(–3, 4) and N(5, –8)?
What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?
What is the slope of a line parallel to MN forM(–3, 4) and N(5, –8)?
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A. B.
C. D.
Warm ups continued
What is the graph of the line that has slope 4 and contains the point (1, 2)?
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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.
Warm ups continued
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3-4 EQUATIONS OF LINESObjective: Write an equation of a line given information about the graph. Solve problems by writing equations.
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Vocabulary
• slope-intercept form
• point-slope form
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Concept
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Example 1Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line.
Slope and y-intercept
y = mx + b Slope-intercept form
y = 6x + (–3) m = 6, b = –3
y = 6x – 3 Simplify.
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Example 1
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.
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TOO
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.
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Example 2
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.
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Example 2 continued
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.
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TOOWrite an equation in point-slope form of the line
whose slope is that contains (6, –3).
A.
B.
C.
D.
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Example 3A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0).
Two Points
Step 1 First, find the slope of the line.
Slope formula
x1 = 4, x2 = –2, y1 = 9, y2 = 0
Simplify.
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Example 3 continued
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):
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Example 3B. Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3).
Two Points
Step 1 First, find the slope of the line.
Slope formula
x1 = –3, x2 = –1, y1 = –7, y2 = 3
Simplify.
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Example 3
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
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Try with a MathleteA. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8).
A.
B.
C.
D.
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TOO
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).
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Example 4
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
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Example 4
Horizontal Line
Point-Slope form
m = 0, (x1, y1) = (5, –2)
Step 2
Answer:
Simplify.
Subtract 2 from each side.y = –2
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TOOWrite an equation of the line through (–3, 6) and (9, –2) in slope-intercept form.
A.
B.
C.
D.
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Horizontal and Vertical Lines
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Homework• Pg. 202 # 13 – 35 odd
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Geometry Warm ups
1) Write two slopes that are parallel
2) Write two slopes that are perpendicular
3) Write two slopes that are neither
4) Write an equation in slope-intercept form of the line with slope -3 and y-intercept 7.
5) What is the slope of the line that goes through points (2, -5) and (4, -5)?
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3 – 4 EQUATIONS OF LINES (DAY 2)Objective: To write equations of lines that are parallel and perpendicular to given lines.
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Example 5
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.
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A. y = 3x
B. y = 3x + 8
C. y = –3x + 8
D.
Example 6
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Example 7Write an equation of a line that is parallel to the line through (4, 0).
Write an equation of a line that is perpendicular to the line through (4, 0).
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Example 8
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.
Write an equation to represent the total cost C for d days of use.
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Homework
• Pg. 203 # 37 – 42 all, 46 – 49 all, 58, 59