Word (.docx)
Acrobat (.pdf)
Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem.
Remarks
Example: For the example 1in benchmark MA.8.A.1.1, graph the equation y = 5w + 25. Tell why the line "slopes up" by 5 each week. Also tell why the line crosses the y-axis at 25.General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 8
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 1 - Analyze and represent linear functions, and solve linear equations and systems of linear equations.
Date Adopted or Revised: 09/07
Content Complexity Rating:
Level 2: Basic Application of Skills & Concepts
-
More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
-
Item Type(s):
This benchmark may be assessed using:
MC
item(s)
- Clarification :
Students will describe the concepts of slope, x-, or y-intercept of a given graph in a real-world situation.
Problems should be solved using concrete or pictorial representations of models, tables, and graphs, rather than solved abstractly using algebraic symbolism. - Content Limits :
Functions may be from all four quadrants.
Items should rely primarily on tables, graphs, and t-tables to present real-world relationships.
Equations used in items should include no more than three operations.
Items may include positive, negative, or zero slopes, but not undefined slopes.
The x- and y-intercepts are limited to integers and halves. - Stimulus Attributes :
Graphics should be used in most of these items, as appropriate.
Items may be set in either a real-world or mathematical context.
Sample Test Items (1)
- Test Item #: Sample Item 1
- Question: The production manager of a furniture manufacturing company plotted values on the graph below to show how the production cost per chair decreases as the number of chairs produced increases. The slope of the dashed line segment joining these points is -1/8.
What does this slope of the dashed line segment represent?
- Difficulty: N/A
- Type: MC: Multiple Choice
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
Related Resources
Vetted resources educators can use to teach the concepts and skills in this benchmark.
Educational Software / Tool
Lesson Plan
Teaching Idea
Student Resources
Vetted resources students can use to learn the concepts and skills in this benchmark.
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.
Teaching Idea
Learning About Rate of Change in Linear Functions Using Interactive Graphs:
This resource features two pairs of interactive graphs to help students explore rate of change and linear relationships. "Users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls." (from NCTM's Illuminations)
Type: Teaching Idea
