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Massachusetts Comprehensive Assessment System

2012, Grade 10 Mathematics

Download PDF Document  Question 17: Open-Response
no calculator allowed
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 y-intercepts 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 "point-slope" or "slope y-intercept" formulas. Explain the significance of a positive, negative, zero, or undefined slope. (AI.P.5)


Line n is represented by the equation below.
y equals four over three x plus four
  1. What is the slope of line n? Show or explain how you got your answer.
  2. What is the y-intercept of line n? Show or explain how you got your answer.
  3. What is the x-intercept 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.
A coordinate plane that has an x and y axis from negative ten to positive ten.
  1. On the coordinate plane you copied into your Student Answer Booklet, graph line n.
  2. Write an equation of the line that has the same x-intercept 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.

ScoreDescription
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 2012 MCAS Sample Student Work: High School Chemistry

Last Updated: April 13, 2020

 
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