1. Lesson 3-4: Equations of Lines
TARGETS
Write an equation of a line given information about the graph.
Solve problems by writing equations.
Targets

2. Nonvertical Line Equations
LESSON 3-3: Equations of Lines
Nonvertical Line Equations
Slope-intercept form
Point-slope form
y = mx + b
Concept

3. Write an equation in slope-intercept Answer:
LESSON 3-3: Equations of Lines
EXAMPLE 1
Slope and y-intercept
Write an equation in slope-intercept
form of the line with slope of 6 and
y-intercept of –3. Then graph the line.
Answer:
y = mx + b Slope-intercept form
y = 6x + (–3) m = 6, b = –3
y = 6x – Simplify.
Use the slope of 6 or to find another point 6 units up and 1 unit right of the y-intercept.
Plot a point at the y-intercept, –3.
Draw a line through these two points.
Example 1

4. LESSON 3-3: Equations of Lines
EXAMPLE 2
Slope and a Point on the Line
Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Then graph the line.
Point-slope form
Answer:
Graph the given point (–10, 8).
Use the slope to find another point 3 units down and 5 units to the right.
Example 2

5. Step 1 First find the slope of the line.
LESSON 3-3: Equations of Lines
EXAMPLE 3
Two Points
A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0).
Step 1 First find the slope of the line.
Slope formula
Step 2 Now use the point-slope form and either point to write an equation.
Point-slope form
Using (4, 9):
Answer:
Example 3

6. Step 1 First find the slope of the line.
LESSON 3-3: Equations of Lines
EXAMPLE 3
Two Points
B. Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3).
Step 1 First find the slope of the line.
Slope formula
Step 2 Now use the point-slope form and either point to write an equation.
Point-slope form
Using (4, 9):
Answer:
Example 3

7. This is a horizontal line.
LESSON 3-3: Equations of Lines
EXAMPLE 4
Horizontal Line
Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form.
Step 1
This is a horizontal line.
Slope formula
Step 2
Answer:
Example 4

8. Horizontal & Vertical Line Equations
LESSON 3-3: Equations of Lines
Horizontal & Vertical Line Equations
Concept

9. y = mx + b Slope-Intercept form 0 = –5(2) + b m = 5, (x, y) = (2, 0)
LESSON 3-3: Equations of Lines
EXAMPLE 5
Write Parallel or Perpendicular Equations of 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.
Example 5

10. A = mr + b Slope-intercept form A = 525r + 750 m = 525, b = 750
LESSON 3-3: Equations of Lines
EXAMPLE 6
Write Linear Equations
RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee.
A. Write an equation to represent the total first year’s 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.
A = mr + b Slope-intercept form
A = 525r m = 525, b = 750
Answer: The total annual cost can be represented by the equation A = 525r
Example 6

11. Evaluate each equation for r = 12.
LESSON 3-3: Equations of Lines
EXAMPLE 6
Write Linear Equations
RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee.
B. Compare this rental cost to a complex which charges a $200 annual maintenance fee but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate?
Evaluate each equation for r = 12.
First complex: Second complex:
A = 525r A = 600r + 200
= 525(12) r = 12 = 600(12) + 200
= 7050 Simplify. = 7400
Example 6

12. LESSON 3-3: Equations of Lines
Write Linear Equations
Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.
Example 6