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.
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.
Solve the following equation
for “y”.
Solve the following equation
for “y”.
3
y  x2
4
You just put the equation in
slope-intercept form!!!
3
y  x2
4
5.3 Equation of Lines
Objectives:
1. Discover the slope intercept
form of the equation of a line.
This graph shows the relationship between
degrees Celsius and degrees Fahrenheit.
This is the
graph of :
9
f  c  32
5
9
y  x  32
5
To convert from C to F, pick some
degrees Celsius to convert:
9
f  c  32
5
Let’s say you want to convert
16°C to °F.
Find 16°C
on the x axis
9
f  c  32
5
Go straight
up from
16° to the
line.
9
f  c  32
5
16 °C = 61°F
9
f  c  32
5
From the
line, go to
the “f” axis.
This is
equal to
16°C in
Fahrenheit!
16 °C = 61°F
9
f  c  32
5
16°C is
equal to
almost 61°
Fahrenheit
You plug 16°C into the
equation and see what you
get.
9
f  c  32
5
f  28.8  32
9 (16)
f 
 32
5 1
f  60.8
You will now be asked
several questions about the
graph of:
9
f  c  32
5
37
3°C= ___°F
Plug 3°C into the equation
and see what you get.
9
f  c  32
5
f  5.4  32
9 (3)
f 
 32
5 1
f  37.4
48
9°C= ___°F
107.6
42°C= _____°F
5
42°F= _____°C
38
100°F= ____°C
Complete the
chart and
calculate the
slope of the
line.
x
y
-2
-4
-1
-1
0
2
1
5
2
8
Compare your calculated slope
with the equation of the line.
Do you see a relationship?
3
1
x
-2
3x+2 -4
-1
-1
The Slope Formula
0
2
1
5
•y2 - y1
x2 - x1
Compare your calculated slope
with the equation of the line.
Do you see a relationship?
The slope
is
the
3
number in
1
front of the
x
-2 -1
1
0
“x”.
2
5
3x+2 -4 -1
When an equation is in
slope-intercept form:
Now look at
the graph of
each line.
Look at
where the
graph crosses
the “y” axis.
What is the
significance
of this
number in
the equation?
This is the yintercept
(where the
graph crosses
the “y” axis.
When an equation is in
slope-intercept form:
Slope-Intercept
Conjecture:
y=mx+b
What is the equation of the
line in slope-intercept form?
3
m =
4
b = -2
3
y  x2
4
What is the equation of the
line in slope-intercept form?
2
m = 
5
b =3
2
y   x3
5
What is the equation of the
line in slope-intercept form?
1
m =
2
b = 4
1
y  x4
2
Graph the equation…. First
calculate the slope and y-int.
2
y  x4
3
2
m =
3
b = -4
Plot the y-intercept.
2
y  x4
3
2
m =
3
b = -4
Apply slope from y-intercept.
2
y  x4
3
2
m =
3
b = -4
Draw line through two points.
2
y  x4
3
2
m =
3
b = -4
Graph each equation:
7
y  x 1
8
7
m =
8
b = 1
Graph each equation:
y=-4x+6
m = -4
b = 6
True or False. The slope of
2
the line below is 5 .
True or False. The yintercept of the line is -4.
True or False. The equation
of the line is:
2
y  x4
5
Homework
Page 275 #’s:
15-45 odds