3.4 Equations of Lines3.4 Equations of Lines

ObjectivesObjectives Write an equation of a line given

information about its graph

Solve problems by writing equations

Equations of LinesEquations of LinesEquations of lines can be written given any of the

following:

The slope and y-intercept

The slope and the coordinates of a point on the line

The coordinates of two points on the line

Equations of LinesEquations of Lines

Slope – Intercept Formy = mx + b

Point – Slope Form

y – y1 = m(x – x1)

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

Example 1:Example 1:

Answer:

Write an equation in point-slope form of the line

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

Simplify.

Point-slope form

Example 2:Example 2:

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.

Example 3:Example 3:

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

Example 3:Example 3:

Point-slope form

Distributive Property

Using (–2, 0):

Simplify.

Answer:

Example 3:Example 3:

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.

Example 4:Example 4:

Point-slope form

Distributive Property

Add 7 to each side.

Answer:

Example 4:Example 4:

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

Example 5a:Example 5a:

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.

Example 5b:Example 5b:

AssignmentAssignment Geometry:

Pg. 148 #16 - 42 evens

Pre-AP Geometry:

Pg. 148 #16 - 44 evens