Academic Content Standards

1
Academic Content Standards

• Patterns, Functions, and Algebra Standard 8th
  Grade
• 1. Relate the various representations of a
  relationship i.e., relate table
• to graph, description and symbolic form.
• 4. Extend the uses of variables to include
  covariants where y depends
• on x.
• 6. Describe the relationship between the graph of
  a line and its
• equation, including being able to explain the
  meaning of slope as a
• constant rate of change and y-intercept in
  real-world problems.

2
Academic Content Standards

• Patterns, Functions, and Algebra Standard 8th
  Grade
• 13. Compute and interpret slope, midpoint and
  distance given a set of
• ordered pairs.
• 15. Describe and compare how changes in an
  equation affects the
• related graphs e.g., for a linear equation
  changing the coefficient of
• x affects the slope and changing the constant
  affects the intercepts.
• 16. Use graphing calculators or computers to
  analyze change e.g.,
• interest compounded over time as a nonlinear
  growth pattern.

3
Solve the following equation for y.
6x 8y 16
-6x
-6x
8y -6x 16
4
Solve the following equation for y.
8y -6x 16
8
8
5
You just put the equation in slope-intercept
form!!!
6
5.3 Equation of Lines

• Objectives
• Discover the slope intercept form of the equation
  of a line.

7
This graph shows the relationship between degrees
Celsius and degrees Fahrenheit.
This is the graph of
8
To convert from C to F, pick some degrees
Celsius to convert
9
Lets say you want to convert 16C to F.
Find 16C on the x axis
10
Go straight up from 16 to the line.
11
From the line, go to the f axis. This is equal
to 16C in Fahrenheit!
16 C 61F
12
16C is equal to almost 61 Fahrenheit
16 C 61F
13
You plug 16C into the equation and see what you
get.
14
You will now be asked several questions about the
graph of
15
37
3C ___F
16
Plug 3C into the equation and see what you get.
17
48
9C ___F
18
107.6
42C _____F
19
5
42F _____C
20
38
100F ____C
21

y 3x 2
Complete the chart and calculate the slope of the
line.
x
-2
-1
0
1
2
y
-4
5
2
8
-1
22
Compare your calculated slope with the equation
of the line. Do you see a relationship?
y 3x 2
slope
x
-2
-1
0
1
-4
5
2
3x2
-1
23
Compare your calculated slope with the equation
of the line. Do you see a relationship?
y 3x 2
The slope is the number in front of the x.
slope
x
-2
-1
0
1
-4
5
2
3x2
-1
24
When an equation is in slope-intercept form
y mx b
slope
25
Now look at the graph of each line. Look at
where the graph crosses the y axis.
y 3x 2
26
What is the significance of this number in the
equation?
y 3x 2
27
This is the y-intercept (where the graph crosses
the y axis.
y 3x 2
28
When an equation is in slope-intercept form
y mx b
slope
y intercept
29
Slope-Intercept Conjecture
ymxb
m slope
b y intercept
30
What is the equation of the line in
slope-intercept form?

m
b
-2
31
What is the equation of the line in
slope-intercept form?
m

3
b
32
What is the equation of the line in
slope-intercept form?

m
b
4
33
Graph the equation. First calculate the slope
and y-int.

m
-4
b
34
Plot the y-intercept.

m
-4
b
35
Apply slope from y-intercept.

m
-4
b
36
Draw line through two points.

m
-4
b
37
Graph each equation

m
1
b
38
Graph each equation

y-4x6
m
-4
b
6
39
True or False. The slope of the line below is
.
40
True or False. The y-intercept of the line is
-4.
It's 4, not -4.
41
True or False. The equation of the line is
42
Homework

• Page 275 s
• 15-45 odds