Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 59185
Writing Equations for Parallel Lines
Students are asked to identify the slope of a line parallel to a given line and write an equation for the line given a point.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, equations, parallel
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WritingEquationsForParallelLines_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Writing Equations for Parallel Lines worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the slope criterion for parallel lines.
Examples of Student Work at this Level
The student is unable to find the slope of
given the slope of the line to which it is parallel.
Questions Eliciting Thinking
What is the slope of a line whose equation is y = If
x + 10?
parallel to this line, what is its slope?
page 1 of 4 Suppose line k is parallel to line j and that the slope of line j is 5. What is the slope of line k?
Instructional Implications
Remind the student that slope is a measure of a line’s “steepness.” Since two lines that are parallel are equally steep, suggest that it is reasonable that their slopes should be
the same. To explore slopes of parallel lines, provide the student with the graphs of parallel lines and ask the student to use the graphs to calculate the slope of each line.
Guide the student through a proof of the criterion for parallel lines.
Moving Forward
Misconception/Error
The student understands the slope criterion for parallel lines but cannot find the slope of a line given its equation in standard form.
Examples of Student Work at this Level
The student:
Correctly identifies the slope of
as
but says that the slope of
is 1 or -3.
Indicates that he or she is unable to find the slope of the line given by the equation in Question 2.
Questions Eliciting Thinking
How did you find the slope of
?
What form is the equation x + 3y =12 written in? Can you read the slope from this equation?
What could you do to find the slope of the line whose equation is x + 3y =12?
Instructional Implications
Review with the student the different forms of equations of lines. Provide the student with several equations written in each form. Have the student identify the equations
written in slope-intercept form. Model rewriting equations in standard or point-slope form in slope-intercept form.
Provide the student with several examples of equations written in standard form or point-slope and ask the student to rewrite each equation in slope-intercept form and
identify its slope as well as the slope of a line parallel to it.
Making Progress
Misconception/Error
The student does not know to or is unable to algebraically find the y-intercept of the line whose equation is to be written.
Examples of Student Work at this Level
The student can find the slope of the line whose equation he or she is writing but is unable to use a given point to write the equation. Instead, the student:
Uses the y-intercepts of the original equations as the y-intercepts of the equations of the parallel lines.
Uses the y-coordinate of the given point (-2,7) as the y-intercept of the equation of the parallel lines.
Estimates the y-intercept by graphing the line using the given point and the slope.
Questions Eliciting Thinking
You said parallel lines have the same slope. Do parallel lines also have the same y-intercept?
page 2 of 4 Why do you suppose you were told the coordinates of B? Is that needed to write the equation of
?
Is (-2, 7) a y-intercept? How can you tell if a point could be a y-intercept?
What if the y-intercept was a rational number such as 6.2? Do you think you could have found it by graphing? Do you know how to find it algebraically?
Instructional Implications
Have the student graph the line given by y=
using its slope,
x+10 using its slope and y-intercept. Then have the student graph the parallel line whose equation is to be written by
, and the given point, (-2, 7). Have the student use the graph to estimate the y-intercept of the parallel line. Then guide the student to find its actual
value algebraically and to write its equation in slope-intercept form. Ask the student to repeat this exercise with the equation given in the second problem. When the
student is finished, ask him or her if there was anything easier about writing the equation of the parallel line in the second problem.
Give the student more practice writing the equations of lines given points and equations of parallel lines written in a variety of forms.
Almost There
Misconception/Error
The student makes a minor algebraic error.
Examples of Student Work at this Level
The student:
Describes the slope of
as
x instead of
.
Leaves the equation in point-slope form instead of writing it in slope-intercept form.
Substitutes the x-coordinate for the y value in the equation and the y-coordinate for the x value in the equation.
Questions Eliciting Thinking
Is slope represented by a number or a term in an equation?
What form is your equation in? What form were you asked to write it in?
I think you made an error when you wrote this equation. Can you review your work and try to find the error?
Instructional Implications
Provide specific feedback to the student regarding his or her error and allow the student to revise the work on his or her paper. Give the student a few examples of
common errors made when writing equations and have him or her identify and correct those errors.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student understands the slope criterion for parallel lines, correctly finds the slope of each line, and uses the given points to write the equations of the lines in slopeintercept form. The student provides the following answers:
page 3 of 4 Questions Eliciting Thinking
What is the slope of a line perpendicular to y=
x + 10?
What can you say about two lines that have the same slope and the same y-intercept?
Instructional Implications
If you have not done so already, introduce the student to the slope criterion for perpendicular lines.
Ask the student to prove the slope criterion for parallel lines. Consider implementing MFAS task Proving the Slope Criterion for Parallel Lines (G-GPE.2.5).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Writing Equations for Parallel Lines worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-GPE.2.5:
Description
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the
equation of a line parallel or perpendicular to a given line that passes through a given point).
Remarks/Examples:
Geometry - Fluency Recommendations
Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric
representations as a modeling tool are some of the most valuable tools in mathematics and related fields.
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