Lesson 3-4 Equations of LinesForm Equation Description

Slope-Intercept

m is the slope, b is the y-intercept

Point-Slope m is the slope, (x1, y1) is a given point

Standard A and B are not both 0. A, B, and C have a GCF of 1. A is usually non-negative.

bmxy )( 11 xxmyy

CByAx

• When finding the equation of a line, we need to be able to fill in the slope and the y-intercept.

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

Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4.

Answer:

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:

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.