1. 3.4 Equations of Lines

2. Objectives
Write an equation of a line given information about its graph
Solve problems by writing equations

3. Equations of Lines
Equations 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

4. Slope – Intercept Form y = mx + b
Equations of Lines
Slope – Intercept Form y = mx + b
Point – Slope Form
y – y1 = m(x – x1)

5. Example 1:
Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3.
Slope-intercept form
Answer: The slope-intercept form of the equation of the line is

6. Example 2:
Write an equation in point-slope form of the line whose slope is that contains (–10, 8).
Point-slope form
Simplify.
Answer:

7. Example 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.

8. Example 3:
Now use the point-slope form and either point to write an equation.
Using (4, 9):
Point-slope form
Distributive Property
Add 9 to each side.

9. Example 3: Using (–2, 0): Point-slope form Simplify.
Distributive Property
Answer:

10. Example 4: the slope of a line perpendicular to it is 2.
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.

11. Example 4: Point-slope form Distributive Property Add 7 to each side.
Answer:

12. Example 5a:
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.
Slope-intercept form
Answer: The total annual cost can be represented by the equation

13. Example 5b:
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.

14. Assignment Pre-AP Geometry: Pg. 148 #16 - 44 evens