Lesson: Standard Linear Form
Length: 52 Minutes
Age or Grade Intended: 9th grade (Algebra I)
Standard 4 — Graphing Linear Equations and Inequalities
Students graph linear equations and inequalities in two variables. They write
equations of lines and find and use the slope and y-intercept of lines. They use
linear equations to model real data.
A1.4.1 Graph a linear equation.
Example: Graph the equation 3x – y = 2.
A1.4.2 Find the slope, x-intercept,
and y-intercept of a line given its graph, its equation, or two points on the line.
Example: Find the slope and y-intercept of the line 4x + 6y = 12.
A1.4.3 Write the equation of a line in slope-intercept
form. Understand how the slope and y-intercept of the graph are related to the equation.
Example: Write the equation of the line 4x + 6y = 12 in slope-intercept form.
What is the slope of this line? Explain your answer.
The standards above are cumulative. In the first three
lessons we worked
with linear graphs, slopes, y-intercepts and the slope intercept form of a linear
equation. In this lesson, we will look at the x-intercept as well as graphing lines
in the standard form.
NOTE: Since these lessons follow the progression of the
text rather than
the sequence of the standards, the information contained in the standards, while
all addressed, are presented in a different order from the standards.
1. All students in the class, given a linear equation in
will identify the x-intercept with 80% accuracy, by correctly providing the answer
for 4 out of 5 assigned problems.
2. All students in the class, given a linear equation in
will graph the equation with 67% accuracy, by correctly graphing 2 out of 3
3. All students in the class, a linear equation in
form will convert the equation to standard form using integers with 75% accuracy, by
correctly providing the answer for 3 out of 4 assigned problems.
Advanced Preparation by Teacher:
The teacher should have the following:
1. An overhead graph transparency with the definitions of x-intercept
2. An overhead graph transparency with an equation in standard form
with a graph of the equation along with a football transparency reusable sticker;
3. An overhead projector with a graph transparency; and,
4. A handout with all of the terms and the definitions of the terms that
the students will have learned in the first four lessons of this unit.
In addition, the students have been assigned to read pages 298 through
300 of their textbook. (ALGEBRA I (2004) Pearson Prentice Hall, Bellman, Bragg
The students will be presented with the transparency of the linear equation
in standard form, and we will review the concept of the intercept. This will be
related to the y-intercept of a line.
Next, we will carry the analogy further, and describe the
as the place where the line crosses the x-axis. The students will be invited to describe
this in terms of our football analogy, and discussion will be allowed. Probable responses
will be a fumble, an incomplete pass or a ball going out of bounds.
This will begin the class with a discussion, to reinforce what we have covered
and to gain the students’ attention. In addition, by allowing the students to create
their own differentiations, it will reinforce the distinction between the x-intercept
and the y-intercept. This introduction will address Gardner’s interpersonal,
spatial and logical-mathematical intelligences as well as bodily kinesthetic for
those students who are more apt to relate to the sports analogy.
The students will first participate in the discussion set
The next step is a directed discussion. Lead the students through the
following questions, guiding them, but letting them stretch their thinking if they
are able to provide the logical progression themselves. This will call for a variety
of Bloom’s taxonomical levels, so the questions may vary as the students provide
their responses. The important point is to guide the students to the end of the
process. Questions: *
1. What is the y-intercept? Knowledge
2. What is the x-intercept? Knowledge
3. How is a slope determined (in terms of shift up and to the right)?
4. What information do we have when we know the y-intercept?
5. What information do we have when we know the x-intercept?
6. With this information, can we graph a line? Evaluation
7. How would we do that? Synthesis
8. If we only had one intercept, say the x-intercept,
would we be able to graph the line? Synthesis
9. So what general statement can we now make when we know the two
intercepts of a line or one of the intercepts and the slope? Synthesis
Answer: with this information, we can graph any linear equation.
At the completion of this discussion, the students will
10 minutes with the teacher graphing linear equations on the overhead. The
teacher will provide the equations, examples of which can be found in the
reading material or the unassigned problems from the end of the section. These
equations will be in the standard form, which enables to students to quickly
calculate the intercepts. As the students assist in graphing the equations, ask
one student to copy each equation onto the blackboard.
At the conclusion of the graphing presentation, return to
and ask the students to relate the terms of each of the equations to the
parameters of the standard form of a linear equation. Bloom’s
Comprehension. Next, have the students explain the difference between a
linear equation in standard form with one in slope intercept form. Bloom’s
Application (Note: the equation in slope intercept form has been solved for the
Have various students come to the board and convert the
standard form to slope-intercept form by solving for the y value. Assist the
students, and draw the class’ attention to correct conversions and how they were
Use the first example and convert it back to standard form
multiplication and addition (subtraction).
Have a different set of students do the same for the
remainder of the
equations on the board. Again, assist the students at the board, and draw the
class’ attention to correct conversions.
At the close of the presentation, give the students an opportunity to ask
any additional questions. Encourage the students with the knowledge that they
now know just about everything that there is to know about drawing lines, and
that it only took four days. Let them know that there is one more form of line,
called the point-slope form that we will cover before the QUIZ, but that with the
progress that they have made so far, this should serve as a review for them.
Assign problems 2, 4, 6, 8, 14, 16, 18, 28, 30, 32, and 34
on page 301 of
the text as class work/homework. Assist the students as needed in solving these
problems during the remainder of the class period.
Adaptation/Enrichment (For LD student(s)):
Although there is a wide variety of different learning disabilities, a common
theme is that time and clarity are always friends with the LD student.
Accordingly, as an accommodation, all of the problems that the class works out
on the overhead can be prepared in advance on a handout, and those students
with an appropriate entry in their IEP would be given the handout so that they
can follow the material presented and process it at their own rate. In addition, a
handout will be prepared for the entire class with the definitions that we have
covered in the first four lessons of this unit. This will allow LD students to review
the terminology that the questions use at their own pace, so that they can more
likely interpret the questions and be able to focus on providing an answer. By
providing class time to complete the homework assignment, LD students will be
given one on one help in understanding the forms of the questions that they will
In this lesson, there is not a real opportunity to allow
an LD student the
opportunity to focus on a particular problem to the exclusion of others so that
they can be an active participant in completing the calculations on the board. If,
however, there is a particular student that is able to do the calculations, but
simply needs more time to reflect on the problem, then that student can be given
a separate assignment with the preceding day’s homework, as extra credit. If the
student has completed the work, then they may participate in those portions of
the class that have them present their calculations on the board.