4-6 graphing linear functions pg. 248. essential question how do you determine if a function is a...
DESCRIPTION
Essential Question How do you determine if a function is a linear function?TRANSCRIPT
4-6 Graphing Linear Functions pg. 248
Essential Question
How do you determine if a function is a linear function?
Graphing Review Video Clip- Standard Deviants
In your notebook:Write down 3 facts from the video clip.
1.2.3.
Definitions• linear equation- an equation whose graph is a line. The solutions of a linear equation are the points that make up its graph.
• linear function-a function whose graph is a non-vertical line.
The graph at right shows how far an inner tube travels down a river if the current flows 2 miles per hour. The graph is linear because all the points fall on a line. It is part of the graph of a linear equation.
Only two points are needed to draw the graph of a linear function. However, graphing a third point serves as a check. You can use a function table to find each ordered pair.
A Function (F) states the relationship between two variables.
( , )( , )2 8
It assigns a rule, that gives a unique
value to y in relation to the value of x.
RuleY = 4x
Function
RO filter RO filter RO filter
Input Rule Output
x 4x y
2
3
4
5
8
12
16
20
Functiony = 4x
4(2)
4(3)
4(4)
4(5)
Rule: y = x
Input outputI’ll push the pedal once.
I’ll push the pedal.
Every time you push the pedal, I’ll square your effort in rotations
2
Function
RO filter RO filter RO filter
Input Rule Output
x x y
2 2
3 3
4 4
5 5
4
9
16
Function
2
25
y = x2
2
2
2
2
Rule: y = 3x
Input output
I’ll give 3 gumballs for every quarter
I’ll push the pedal once.
I’ll put quarters in.
Function
RO filter RO filter RO filter
Input Rule Output
x 3x y
2 3(2)
3 3(3)
4 3(4)
5 3(5)
6
9
12
15
Functiony = 3x
x
y
0–2–4 2 4
2
4
–2
–4
Graph the linear function y = 4x - 1.Example 1
Input Rule Output Ordered Pair
x 4x – 1 y (x, y)
0
1
–1
4(0) – 1
4(1) – 1
4(–1) – 1
–1
3
–5
(0, –1)
(1, 3)
(–1, –5)
(0, –1)
(1, 3)
(–1, –5)
Graph the linear function y = 3x + 1.Input Rule Output Ordered Pair
x 3x + 1 y (x, y)
0
1
–1
3(0) + 1
3(1) + 1
3(–1) + 1
1
4–2
(0, 1)
(1, 4)
(–1, –2)
Example 2
x
y
0–2–4 2 4
2
4
–2
–4
(0, 1)
(1, 4)
(–1, –2)
The fastest-moving tectonic plates on Earth move apart at a rate of 15 centimeters per year. Scientists began studying two parts of these plates when they were 30 centimeters apart. Write a linear function that describes the movement of the plates over time. Then make a graph to show the movement over 4 years.
Example 3
Input Rule Output15(x) + 30x
0
2
4
15(0) + 30
15(2) + 30
15(4) + 30
y
30
60
90
x
y100
80
60
40
20
0 2 4 8 10 12
Cent
imet
ers
Years
Graphing Linear Equations Brain-Pop
Write down 2 facts about graphing linear equations.1.2.
Work Session
Linear Contemplations Worksheet Follow along as we review the directions
Homework
Workbook pg. 41All problems
Closing
The temperature of a liquid is decreasing at a rate of 12°F per hour. Susan begins measuring the liquid at 200°F. Write a linear function that describes the change in temperature over time. Then make a graph to show the temperature over 5 hours.
y = 200 – 12x