1. Linear Relations

2. Linear Relations
Formula: a mathematical statement that shows a relationship between specific quantities. Ex. A = πr2 Area of a circle radius r

3. Example 1: Graph from a Linear Formula
Sound travels 1500 m/s in salt water. This relationship can be express by the formula d = 1500t, where d is the distance travelled, in meters, and t is the time, in seconds.
a) Make a table of Values and then Graph the values. d
8000
7000
6000
5000
4000
3000
2000
1000 t d 1
1500 2
3000 3
4500 4
6000 5
7500 6
9000 7
10500
d = 1500(t)
d = 1500(1)
d = 1500
1st letter (answer of the formula) goes to the 2nd column
Distance (m) t
b) Is it reasonable to have points between the ones on this graph?
   Yes
c) Calculate the distance sound travels in 3.5 seconds?
d = 1500t
d = 1500 (3.5)
d = 5250 m
Sound travels 5220 meters in 3.5 seconds.
Time (s)

4. a) Make a table of Values and then Graph the values.
Example 2 - James rents a lawnmower for $8 per hour. A formula representing this relationship is C = 8t, where C is the rental cost, in dollars, and t is the time, in hours.
 a) Make a table of Values and then Graph the values. d 64 56 48 40 32 24 16 8 t C 1 8 2 16 3 24 4 32 5 40 6 48
C = 8(t)
c = 8 (0)
c = 8
Cost ($)
b) Is it reasonable to have points between the ones on this graph?
Maybe, but can you really rent it for half an hour?
c) Calculate the cost to rent for 12 hours?
C = 8t
C = 8(12)
C = 96
Cost to rent the lawnmower is $96 t
Time( h)

5. y
Example 3 – Graph from a Linear Equation Using Integers
Use the linear equation y = -3x + 4 to complete the flowing steps.
 a) Make a table of Values and then Graph the values. x y -2 10 -1 7 4 +1 1 +2
y = -3x + 4
y = -3(-2) + 4
y = 6 + 4
y = 10
coordinate (point on graph or table) x
b) Determine the value for y in the order pair (11, y).
y = -3x + 4
= -3(11) + 4 =
= -29
y = -3x + 4

6. Look off the table of values or off the graph (0,3)
y-axis
Example 4 – Graph from a Linear Equation Using Integers
Use the linear equation y = 2x + 3 to complete the flowing steps.
 a) Make a table of Values and then Graph the values.
y = -2x + 3 x y -2 -1 1 3 +1 5 +2 7
y = 2x + 3
y = 2(-2) + 3
y =
y = -1
x-axis
b) What are the coordinates for the point that would lie on the y-axis?
Look off the table of values or off the graph
(0,3)
Algebraically use formula y = 2x +3
x = 0
y = 2(0) + 3

7. 9.3 Linear Relation