1. Equation of a Line
Thm. A line has the equation y = mx + b, where m = slope and b = y-intercept.
 This is called Slope-Intercept Form
Ex. Find the slope and y-intercept:
y = 3x + 1
2x + 3y = 1

2. Ex. Graph: a)

3. Ex. Graph: b)

4. Ex. Graph: c)

5. Slope Thm. The slope between (x1,y1) and (x2,y2) is
Ex. Find the slope between (-2,0) and (3,1).

6. Rising line has positive slope:
Falling line has negative slope:
Horizontal line as slope of 0:
Vertical line has undefined slope:
A vertical line has an equation like x = 3, and can’t be written as y = mx + b

7. Thm. Parallel lines have the same slope.
Thm. Perpendicular lines have slopes that are negative reciprocals.
Ex. Are the lines parallel, perpendicular, or neither?
(3,-1) to (-3,1) and (0,3) to (-1,0)

8. Thm. A line with m = slope that passes through the point (x1,y1) has the equation
y – y1 = m(x – x1)
This is called Point-Slope Form
Ex. Write the equation in Slope-Intercept Form:
slope = 3, contains (1,-2)

9. Ex. Write the equation in Slope-Intercept Form:
b) contains (2,5) and (4,-1)

10. Ex. Find equation of the lines that pass through (2,-1) are:
parallel to, and
perpendicular to, the line 2x – 3y = 5

11. Ex. The maximum slope of a wheelchair ramp is
Ex. The maximum slope of a wheelchair ramp is A business is installing a ramp that rises 22 in. over a horizontal distance of 24 ft. Is the ramp steeper than required?

12. Ex. An appliance company determines that the total cost, in dollars, of producing x blenders is
C = 25x
Explain the significance of the slope and y-intercept.

13. Ex. A college purchases exercise equipment worth $12,000
Ex. A college purchases exercise equipment worth $12,000. After 8 years, the equipment is determined to have a worth of $ Express this relationship as a linear equation. How many years will pass before the equipment is worthless?

14. Practice Problems
Section 2.1
Problems 9, 21, 41, 51, 69, 107, 109

15. Functions
Def. (formal) A function f from set A to set B is a relation that assigns to each element x in set A exactly one element y in set B.
Def. (informal) A set of ordered pairs is a function if no two points have the same x-coordinate

16. x is called the independent variable
Set A
(the x’s)
The input
Domain
Set B
(the y’s)
The output
Range
x is called the independent variable
y is called the dependent variable

18. Ex. Determine whether the relation is a function: a)b) 4 -3 7 5 y 3 -1 2 x

19. Ex. Determine whether the relation is a function:
c) x is the number of representatives from a state, y is the number of senators from the same state
d) x is the time spent at a parking meter, y is the cost to park

20. Ex. Determine whether the relation is a function:
e) x2 + y = 1
f) x + y2 = 1

21. Rather than writing
y = 7x + 2
we can express a function as
f (x) = 7x + 2
 This is called Function Notation

22. Ex. Let g(x) = -x2 + 4x + 1, find
a) g(2)
b) g(t)
c) g(x + 2)

23. The next example is called a piecewise function because the equation depends on what we are plugging in.
Ex. Let , find f (-1), f (0), and f (1).

24. Finding the domain means determining all possible x’s that can be put into the function
Ex. Find the domain of the function
f : {(-3,0), (-1,4), (0,2), (2,2), (4,-1)}

25. Often, finding the domain means finding the x’s that can’t be used in the function
Ex. Find the domain of the function a)
b) Volume of a sphere:

26. Ex. Find the domain of the function

27. Ex. You’re making a can with a height that is 4 times as long as the radius. Express the volume of the can as a function of height.

28. Ex. When a baseball is hit, the height of a baseball is given by the function f (x) = x2 + x + 3, where x is distance travelled (in ft) and f (x) is height (in ft). Will the baseball clear a 10-foot fence that is 300 ft from home plate?

29. Ex. For f (x) = x2 – 4x + 7, find

30. Practice Problems
Section 2.2
Problems 9, 15, 29, 35, 59, 79, 87, 93