Lesson 3-4

Equations of Lines

5-Minute Check on Lesson 3-35-Minute Check on Lesson 3-35-Minute Check on Lesson 3-35-Minute Check on Lesson 3-3 Transparency 3-4

Find the slope of each line for M(–3, 4) and N(5, –8).

1. MN 2. a line perpendicular to MN 3. a line parallel to MN

Graph the line that satisfies each condition.

4. slope = 4 and 5. slope = 0 andcontains (1, 2) contains (–3, –4)

6. Use slope to find a relationship between CD and EF for C(4, 5), D(–1, 15), E(–4, –6), F(0, –8).

Standardized Test Practice:

A

C

B

D

CD || EF CD EF

neither || nor not enough information given

–3/2 2/3 –3/2

C

Objectives

• Write an equation of a line given information about its graph

• Solve problems by writing equations

Vocabulary:Equations of Lines

• Slope – Intercept Form:

y = mx + b

• Point Slope Form:

y – y1 = m(x – x1)

• From two points:(y2 – y1)

y – yp = –––––––– (x – xp)(x2 – x1)

m is the slopeb is the y-intercept

m is the slope(x1,y1) is the given point

(y2 – y1) / (x2 – x1) is the slopep is one of the given points

Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3.

Answer: The slope-intercept form of the equation of the line is

Slope-intercept form

Answer:

Write an equation in point-slope form of the line

whose slope is that contains (–10, 8).

Simplify.

Point-slope form

Answer:

Write an equation in point-slope form of the line

whose slope is that contains (6, –3).

Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0).

Find the slope of the line.

Slope formula

Simplify.

Now use the point-slope form and either point to write an equation.

Point-slope form

Add 9 to each side.

Using (4, 9):

Distributive Property

Point-slope form

Distributive Property

Using (–2, 0):

Simplify.

Answer:

Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8).

Answer:

Write an equation in slope-intercept form for a line containing (1, 7) that is perpendicular to the line

the slope

of a line perpendicular to it is 2.

Point-slope form

Distributive Property

Add 7 to each side.

Answer:

Write an equation in slope-intercept form for a line containing (–3, 4) that is perpendicular to the line

RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Write an equation to represent the total annual 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.

Answer: The total annual cost can be represented by the equation

Slope-intercept form

RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Compare this rental cost to a complex which charges a $200 security deposit but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate?

First complex: Second complex:

Simplify.

Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.

Answer:

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.

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?

Answer: The first company offers the better rate. Nine days cost $325 instead of $365.

Summary & Homework

• Summary:– An equation of a line can be written if you are

given: • The slope and the y intercept, or • The slope and the coordinates of a point on the line, or • The coordinates of two points on the line

– Slope – Intercept Form: y = mx + b

– Point Slope Form: y – y1 = m(x – x1)

• Homework: pg 148-149: 15-19, 21, 35, 37, 47