1. 3-4 Equations of Lines You found the slopes of lines.
Write an equation of a line given information about the graph.
Solve problems by writing equations.

2. Writing an Equation of a Line
Slope-intercept form
Given the slope m and the y-intercept b,
y = mx + b
Point-slope form
Given the slope m and a point (x1,y1)
y − y1 = m(x−x1)
Two points
Given two points (x1,y1) and (x2,y2)

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4. Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line.
y = mx + b Slope-intercept form
y = 6x + (–3) m = 6, b = –3
y = 6x – Simplify.

5. Answer:
Plot a point at the y-intercept, –3.
Use the slope of 6 or to find another point 6 units up and 1 unit right of the y-intercept.
Draw a line through these two points.

6. 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
Simplify.

7. Graph the given point (–10, 8).
Use the slope to find another point 3 units down and 5 units to the right.
Draw a line through these two points.

8. 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
x1 = 4, x2 = –2, y1 = 9, y2 = 0
Simplify.

9. Step 2 Now use the point-slope form and either point to write an equation.
Using (4, 9):
Distributive Property
Add 9 to each side.
Answer:

10. 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
x1 = –3, x2 = –1, y1 = –7, y2 = 3
Simplify.

11. Step 2 Now use the point-slope form and either point to write an equation.
Using (–1, 3):
m = 5, (x1, y1) = (–1, 3)
Distributive Property
Add 3 to each side.
y = 5x + 8
Answer:

12. Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form.
Step 1
Slope formula
This is a horizontal line.
Step 2
Point-Slope form
m = 0, (x1, y1) = (5, –2)
Simplify.
Subtract 2 from each side.
y = –2
Answer:

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14. Parallel lines that are not vertical have equal slopes.
Two non-vertical lines are perpendicular if the product of their slope is -1.
Vertical and horizontal lines are always perpendicular to one another.

15. Write Equations of Parallel or Perpendicular 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.

16. 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

17. 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
Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.

18. 3-4 Assignment
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