




Massachusetts Comprehensive Assessment System
2012, Grade 10 Mathematics
Question 17: OpenResponse 

Reporting Category: Patterns, Relations, and Algebra Standard: 10.P.2  Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x and yintercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the "pointslope" or "slope yintercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope. (AI.P.5) 
Line n is represented by the equation below.  What is the slope of line n? Show or explain how you got your answer.
 What is the yintercept of line n? Show or explain how you got your answer.
 What is the xintercept of line n? Show or explain how you got your answer.
A coordinate plane is shown below. Copy the axes and the labels of the coordinate plane exactly as shown onto the grid in your Student Answer Booklet. On the coordinate plane you copied into your Student Answer Booklet, graph line n.
 Write an equation of the line that has the same xintercept as line n and a slope of –2. Show or explain how you got your answer.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Patterns, Relations, and Algebra concepts involved in determining a line’s slope and x  and y intercepts from a linear equation that represents the line. The student graphs a line and writes an equation for a line that has a different slope and the same x intercept as the graphed line. 
4 
3 
The student response demonstrates a good understanding of the Patterns, Relations, and Algebra concepts involved in determining a line’s slope and x  and y intercepts from a linear equation that represents the line. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points. 
2 
The student response demonstrates fair understanding of the Patterns, Relations, and Algebra concepts involved in determining a line’s slope and x  and y intercepts from a linear equation that represents the line. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates only minimal understanding of the Patterns, Relations, and Algebra concepts involved in determining a line’s slope and x  and y intercepts from a linear equation that represents the line. 
0 
The student response contains insufficient evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in determining a line’s slope and x  and y intercepts from a linear equation that represents the line to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Patterns, Relations, and Algebra
 Question 20: Data Analysis, Statistics, and Probability
 Question 21: Number Sense and Operations
 Question 31: Data Analysis, Statistics, and Probability
 Question 41: Patterns, Relations, and Algebra
 Question 42: Measurement
Return to the MCAS 2012 Student Work Directory
Last Updated: February 13, 2015


