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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)?
A. B.
C. D.
Warm ups continued
What is the graph of the line that has slope 4 and contains the point (1, 2)?
What is the graph of the line that has slope 0 and contains the point (–3, –4)?
A. B.
C. D.
Warm ups continued
3-4 EQUATIONS OF LINESObjective: Write an equation of a line given information about the graph. Solve problems by writing equations.
Vocabulary
• slope-intercept form
• point-slope form
Concept
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.
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.
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.
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.
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.
TOOWrite an equation in point-slope form of the line
whose slope is that contains (6, –3).
A.
B.
C.
D.
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.
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):
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.
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
Try with a MathleteA. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8).
A.
B.
C.
D.
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).
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
Example 4
Horizontal Line
Point-Slope form
m = 0, (x1, y1) = (5, –2)
Step 2
Answer:
Simplify.
Subtract 2 from each side.y = –2
TOOWrite an equation of the line through (–3, 6) and (9, –2) in slope-intercept form.
A.
B.
C.
D.
Horizontal and Vertical Lines
Homework• Pg. 202 # 13 – 35 odd
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)?
3 – 4 EQUATIONS OF LINES (DAY 2)Objective: To write equations of lines that are parallel and perpendicular to given lines.
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.
A. y = 3x
B. y = 3x + 8
C. y = –3x + 8
D.
Example 6
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).
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.
Homework
• Pg. 203 # 37 – 42 all, 46 – 49 all, 58, 59