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

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