This document provides information about key concepts related to analyzing relationships between tables, graphs, and equations. It discusses how to determine slope from two points on a line graph or in a table, how to identify the y-intercept and x-intercept of a line graph, and how to write the equation of a line given its slope and a point. Examples are provided to illustrate how to convert between tabular, graphical, and equation forms of linear relationships. Connections between these representations are emphasized.

1. Tables, Graphs, & Equations
Cheryl Cresci
Department of Education Math Standard 2-
End
Show
Algebraic Reasoning.
Grade 8:
Determine the slope of a line given two points on the line (as coordinates, in a graph, in a table)
Use y-intercept and slope to graph the equation of a line
Compare the rates of change in tables and graphs and classify them as linear or nonlinear
Write an equation given the tabular or graphic form of a linear problem
Analyze the interrelationships among tables, graphs, and equations of lines, paying particular attention to the meaning
of intercept and slope in the context of the problem

2. The Coordinate Graph
To Review Basics
Click Here
15
Distance (thousand Height
feet) (thousand feet)
10 Slope
TABLES
TABLES
5
-15 -10 -5 5 10 15
-5
End Show INTERCEPTS
ORDERED
-10 PAIRS
-15 Functions

3. Click Y-axis
Herehttp://ww
w.printfreegr
aphpaper.co For Practice
m/ to Print Activity
Graph Paper Click Here
5
Explaining the Basics of a Cartesian Graph
Click Here
(Try some of the interactive activities at this site as well!)
-5 (0,0) Origin 5 X-axis
-5

4. Print Graph
Paper
http://www.print
freegraphpaper.c
om/
Practice making and using your own graph:
Click Here
1. Make the x-axis and label with integers.
2. Make the y-axis and label with integers.
3. Label the four quadrants.
4. Make a simple drawing and list the order pairs on a separate sheet.
5. Give the list of ordered pairs to a partner and see if they
re-create your original drawing. (Don’t let them see your picture
ahead!)
Click here to
Coordinate Graph Lesson
Click Here
next review
Tables

5. Distance (thousand feet) Height
(thousand feet)
Collected data can be entered into a table to then create
ordered pairs, lines on a graph, and equations.

6. We could use a table to chart the height of the flowers as
time passes.

7. Day(s) 1 2 3 4 5 6 7 8 9 10
Height 2 4 6 8 10 12 14 16 18 20
(mm)
This flower is growing at a constant rate; therefore, it is
linear. If it is not growing at a constant rate it is non-
linear.

8. We can create a table showing the distance traveled with time……

9. Hour(s) 1 2 3 4
Distance 25,000 40,000 55,000 70,000
(Km)
Click Here to
Review
ordered Pairs
This airplane is traveling at a constant rate; therefore it is linear.

10. Video on Graphing Ordered Pairs
Click here

11. This table can be listed as ordered pairs
Day(s) 1 2 3 4 5 6 7 8 9 10
x
Height (mm) 2 4 6 8 10 12 14 16 18 20
Y
The ordered pairs would be: (x, y)
(1,2)
(2,4)
(3,6)
(4,8)
(5,10)
(6,12)
(7,14)
(8,16)
(9,18)
(10,20)

12. This table can be turned into ordered pairs:
Hour(s) 1 2 3 4
Distanc 25,000 40,000 55,000 70,000
e (Km)
The ordered pairs would be:
(x, y)
(1, 25,000)
(2, 40,000)
(3, 55,000)
(4, 70,000)

13. Graphing Ordered Pairs
(click for review)
Use a separate graph for each.
(x, y)
(1,2) (x, y)
(2,4) (1, 25,000)
(3,6) (2, 40,000)
(4,8) (3, 55,000)
(5,10) (4, 70,000)
(6,12)
(7,14)
(8,16)
(9,18)
(10,20)
Click Here if
ready for to
learn Slope Plot the ordered pairs on graph paper and connect to form a line. If a
straight line forms than this graph is linear.

14. Slope Tutorial
Click Here

15. How much is the flower growing each day?
Day(s) 1 2 3 4 5 6 7 8 9 10
Height 2 4 6 8 10 12 14 16 18 20
(mm)

16. The amount it is growing is 2mm per day.
This is the rate of change.
The rate of change is also called the slope of
the line.

17. y
Slope can be found 20
15
from knowing either
Height
10
one of these: 5
-10 -5 5 10 x
-5 Day(s)
a. Two ordered pairs on a -10
graph line.
b. Two ordered pairs on a
table.
Can you determine the slope?
Click on Video Lesson to learn
how.
Video Lesson on Slope
Click Here

18. Slope =
Slope = change in Y
change in X
Use your knowledge gained from the video lesson on slope and
Determine the slope of the line for the flower example.

19. (You could use any two ordered pairs and you
would get the same answer for slope.)
If you used the ordered pairs (1,2) and
(10, 20):
20 - 2
10 - 1
18
9
18 divided by 9
Slope =2
Can you also see that you can use the rate of change in the table as the slope?
Day(s) 1 2 3 4 5 6 7 8 9 10
Height 2 4 6 8 10 12 14 16 18 20
(mm)

20. What is the rate of change?
Hour(s) 1 2 3 4
Distance 25,000 40,000 55,000 70,000
(Km)
Ready for
Intercepts
Determine the slope of the line from two Click Here
ordered pairs on the graph & compare.

21. Intercepts
Click Here

22. Y-intercept …… is where the line crosses the Y-axis.
X-intercept…….is where the line crosses the x-axis.

23. Click Here for Video on X & Y Intercepts
Click Here
when
ready to
learn Click Here for a Lesson on X & Y Intercepts
about
Equations (Try some of the practice problems.)

24. Can you determine the intercepts?
Day(s) 1 2 3 4 5 6 7 8 9 10
x
Height 2 4 6 8 10 12 14 16 18 20
(mm)
y

25. The y-intercept is 0. The x-intercept is 0.
Click Here
when ready
to learn
about
Equations

26. Y= -5x + 17
Y=2x + 4
EQUATIONS
Click Here
3x + 4y =10
-9x + 3y =27

27. There is more than one way to find the equation of a line.
Equations of a straight
line.
Point-Slope Formula Click Here
Click Here
Video Lesson on Writing Equation Given a Point and the Slope
Video on Graphing an Equation
Click Here

28. If the slope is 2 and passes through the point (2,4)
What is the equation of this line?
( Use knowledge from watching video lesson
and web page lesson.)

29. The equation is: Y=2x
Day(s) 1 2 3 4 5 6 7 8 9 10
x
Height 2 4 6 8 10 12 14 16 18 20
(mm)
y
Can you also see how you could plug in the value
for x into the equation, solve, and obtain Y value?

30. If the slope of the line is 15, 000 and passes through the
Point (2, 40,000) ….What is the equation of the line?

31. The equation is:
Y=15,000x + 10,000

32. Can you see connections?
Tables
Ordered Pairs
Graphs
Slope
Intercepts
Equations
Functions
Go back and review any section you are not confident with yet…. Review

33. The End