V-1
STANDARD V: The student will be able to apply graphing techniques.
OBJECTIVE 1: Graph or identify graphs of linear equations.
ELIGIBLE CONTENT: Equations may be expressed in terms of f(x).
The options may be four graphs.
The options may be four equations.
NUMBER OF TEST ITEMS: Objectives 1 and 4 contain a total of 6 questions.
LOCATION OF OBJECTIVE
SUBJECT WITHIN THE COURSE OF STUDY PAGE
8th Grade Math 31. Identify and graph functions on the Cartesian plane. 66
Introduction 23. Graph linear functions in the form y = mx + b on the
to Algebra Cartesian plane. 76
18. Graph linear equations written in standard form or
Algebra I slope-intercept form. 82
PREREQUISITE SKILLS OR RELATED SKILLS FOR THIS
SUBJECT OBJECTIVE WITHIN THE COURSE OF STUDY PAGE
5th Grade Math 36. Identify coordinates on grids, graphs, and maps. 46
6th Grade Math 36. Identify and plot coordinates on grids, graphs, and maps. 52
31. Draw geometric figures on the Cartesian plane and identify
coordinates of vertices. 58
32. Explore vertical and horizontal distances and slope on the
Cartesian plane. 58
34. Use computers and graphing calculators to facilitate
understanding of coordinate geometry and other
PATHWAYS FOR LEARNING - MATHEMATICS C-80
V-1
7th Grade Math mathematical concepts. 58
28. Identify components of the Cartesian plane. 65
30. Use computers and graphing calculators to facilitate
8th Grade Math understanding of coordinate geometry. 66
PATHWAYS FOR LEARNING - MATHEMATICS C-81
V-1
PREREQUISITE SKILLS OR RELATED SKILLS FOR THIS
SUBJECT OBJECTIVE WITHIN THE COURSE OF STUDY (cont.) PAGE
Introduction 20. Demonstrate proficiency in using vocabulary and basic
to Algebra concepts related to the coordinate plane. 76
13. Apply the terminology associated with the Cartesian plane to
the graphing of equations. 81
17. Graph lines given two points or a slope and a point. 82
Algebra I 19. Graph systems of linear equations. 82
*Algebra II 17. Graph basic equations and identify the graphs of basic
with Trig. equations in the coordinate plane. 95
*Expansion/Review Material
TEACHER OVERVIEW
The student will need to recognize a given equation’s graph and will also need to recognize
an equation given a certain graph. To do this, the student should graph a line using more
than one method. For a quick review, students can use a graphing calculator to demonstrate
graphs of equations. However, graphing calculators will not be allowed on the graduation
examination.
ACTIVITY: Coordinate Classroom
(Reference the activity from Standard IV, Objective 2.)
Purpose: To graph a line on a coordinate plane
Materials/Equipment:
Desks or chairs
Coordinate grid paper (graph paper)
Crepe paper (three different colors)
PATHWAYS FOR LEARNING - MATHEMATICS C-82
V-1
Procedure:
As a continuation of the coordinate room activity, have groups of students “graph” a line.
1. Given an equation, have a student stand on the x-intercept and a second student stand on
the y-intercept. The two students will stretch crepe paper between them to represent
the line. (Give the students the x-intercept and the y-intercept to begin. Then give
them an equation and have them determine the intercepts.) After several examples,
have the students graph the examples on the coordinate grid paper.
2. Give an equation in slope-intercept form (y = mx + b). Have one student begin on the
y-intercept and have another student “move” the slope to a second point. (Remember,
slope can be defined as “rise over run.”) Have a third student begin at the y-intercept
and “move” the slope in the opposite direction and show that all of them are still on the
same line. Explain that another representation for the slope-intercept form y = mx + b is
f(x) = mx + b. Develop student understanding that y and f(x) represent the value of y for
a given value of x. The equation may be written in either format.
3. Graph a vertical line and a horizontal line using at least five students for each. Draw
several graphs of vertical lines and several graphs of horizontal lines. Help students
recognize that the graph of any vertical line will be represented by an equation in the
form x = c and that horizontal lines will be represented by an equation in the form y = c.
4. Proceed from this activity into examples of the type specified in the eligible content.
After discussing the examples, assign problems for students to work on their own. These
problems should specifically target skills involved in graphing linear equations.
Give the students an equation in slope-intercept form (y = mx + b) to
graph.
Give the students an equation in standard form (ax + by = c) to graph.
Give students the graph of a line. Ask them to write the equation of that
line.
Give students four graphs of equations of lines and one equation that is
illustrated in one of the graphs. Ask them to match the equation to the
correct graph.
Questions:
1. Explain how the second and third student can move in opposite directions in the activity
above and still be on the same line. [Answer: Each student is moving in a positive or
PATHWAYS FOR LEARNING - MATHEMATICS C-83
V-1
negative direction. For example, a positive slope can “rise up” (+) and “run right” (+) or
( ) . A positive slope can also “rise down” () and “run left” () or ( ).]
2. Why is the equation of a horizontal line y = c and the equation of a vertical line x = c ?
(Answer: A horizontal line is y = c because all of the y values are constant. Y is the
same for any value of x. A vertical line is x = c because all of the x values are constant.
X is the same for any value of y.)
3. What is the slope of a vertical line? (Answer: undefined or “no slope”) What is the
slope of a horizontal line? (Answer: zero)
Reading/Writing Connection:
Reading Comprehension Standard II, Objective 3: Determine cause and effect.
Write a paragraph explaining the graphs and equations of vertical and horizontal lines.
Explain the connection of the graphs to the equations.
PATHWAYS FOR LEARNING - MATHEMATICS C-84