NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 20
8•4
Lesson 20: Every Line Is a Graph of a Linear Equation
Classwork
Opening Exercise
Figure 1
Figure 2
Lesson 20:
Every Line Is a Graph of a Linear Equation
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
S.117
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 20
8•4
Exercises
1.
Write the equation that represents the
line shown.
Use the properties of equality to change
the equation from slope-intercept form,
𝑦 = 𝑚𝑥 + 𝑏, to standard form,
𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are
integers, and 𝑎 is not negative.
2.
Write the equation that represents the line
shown.
Use the properties of equality to change
the equation from slope-intercept form,
𝑦 = 𝑚𝑥 + 𝑏, to standard form,
𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are
integers, and 𝑎 is not negative.
Lesson 20:
Every Line Is a Graph of a Linear Equation
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
S.118
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
3.
Lesson 20
8•4
Write the equation that represents the
line shown.
Use the properties of equality to change
the equation from slope-intercept form,
𝑦 = 𝑚𝑥 + 𝑏, to standard form,
𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are
integers, and 𝑎 is not negative.
4.
Write the equation that represents the
line shown.
Use the properties of equality to change
the equation from slope-intercept form,
𝑦 = 𝑚𝑥 + 𝑏, to standard form,
𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are
integers, and 𝑎 is not negative.
Lesson 20:
Every Line Is a Graph of a Linear Equation
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
S.119
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
5.
Lesson 20
8•4
Write the equation that represents the
line shown.
Use the properties of equality to change
the equation from slope-intercept form,
𝑦 = 𝑚𝑥 + 𝑏, to standard form,
𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are
integers, and 𝑎 is not negative.
6.
Write the equation that represents the
line shown.
Use the properties of equality to
change the equation from slopeintercept form, 𝑦 = 𝑚𝑥 + 𝑏, to
standard form, 𝑎𝑥 + 𝑏𝑦 = 𝑐, where
𝑎, 𝑏, and 𝑐 are integers, and 𝑎 is not
negative.
Lesson 20:
Every Line Is a Graph of a Linear Equation
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
S.120
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 20
8•4
Lesson Summary
Write the equation of a line by determining the 𝑦-intercept point, (0, 𝑏), and the slope, 𝑚, and replacing the
numbers 𝑏 and 𝑚 into the equation 𝑦 = 𝑚𝑥 + 𝑏.
Example:
The 𝑦-intercept point of this graph is (0, −2).
The slope of this graph is 𝑚 =
4
= 4.
1
The equation that represents the graph of this line is 𝑦 = 4𝑥 − 2.
Use the properties of equality to change the equation from slope-intercept form, 𝑦 = 𝑚𝑥 + 𝑏, to standard form,
𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are integers, and 𝑎 is not negative.
Lesson 20:
Every Line Is a Graph of a Linear Equation
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
S.121
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 20
8•4
Problem Set
1.
Write the equation that represents the
line shown.
Use the properties of equality to change
the equation from slope-intercept form,
𝑦 = 𝑚𝑥 + 𝑏, to standard form,
𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are
integers, and 𝑎 is not negative.
2.
Write the equation that represents the line shown.
Use the properties of equality to change the equation
from slope-intercept form, 𝑦 = 𝑚𝑥 + 𝑏, to standard
form, 𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are integers, and
𝑎 is not negative.
Lesson 20:
Every Line Is a Graph of a Linear Equation
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
S.122
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
3.
Lesson 20
8•4
Write the equation that represents the line shown.
Use the properties of equality to change the equation from
slope-intercept form, 𝑦 = 𝑚𝑥 + 𝑏, to standard form, 𝑎𝑥 +
𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are integers, and 𝑎 is not negative.
4.
Write the equation that represents the line
shown.
Use the properties of equality to change the
equation from slope-intercept form, 𝑦 = 𝑚𝑥 + 𝑏,
to standard form, 𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐
are integers, and 𝑎 is not negative.
Lesson 20:
Every Line Is a Graph of a Linear Equation
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
S.123
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
5.
Lesson 20
8•4
Write the equation that represents the line
shown.
Use the properties of equality to change
the equation from slope-intercept form,
𝑦 = 𝑚𝑥 + 𝑏, to standard form,
𝑎𝑥 + 𝑏𝑦 = 𝑐, where 𝑎, 𝑏, and 𝑐 are
integers, and 𝑎 is not negative.
6.
Write the equation that represents the line
shown.
Use the properties of equality to change the
equation from slope-intercept form,
𝑦 = 𝑚𝑥 + 𝑏, to standard form, 𝑎𝑥 + 𝑏𝑦 = 𝑐,
where 𝑎, 𝑏, and 𝑐 are integers, and 𝑎 is not
negative.
Lesson 20:
Every Line Is a Graph of a Linear Equation
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
S.124
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.