School Improvement in Maryland
Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 1.0 Knowledge of Algebra, Patterns, and Functions

Topic C. Numeric and Graphic Representations of Relationships

Indicator 2. Analyze linear relationships

Objective a. Determine the slope of a graph in a linear relationship

Assessment limit: Use an equation with integer coefficients (-9 to 9) and integer constants (-20 to 20) and a given graph of the relationship

Clarification

Slope is the ratio of the vertical change to the horizontal change of a graph in a linear relationship. To determine the slope:

  • Identify two points on the linear graph
  • Determine the vertical change by finding the difference between the y-coordinates of both points and then find the horizontal change by finding the difference between the x-coordinates of both points.

    equation image
     
  • Note that the order in which the differences are taken must be the same for both the y-coordinates and the x-coordinates.
  • Be sure that the difference between the y-coordinates (vertical change) is divided by the difference between the x-coordinates (horizontal change).

Classroom Example 1

Determine the slope of the line in the graph below.

chart image

Answer:

Find two points on the graph, for example, (0, 4) and (-1, 0). Determine the ratio of the vertical change to the horizontal change.

equations image

Use a grid for the coordinates of the points to determine the slope.
Visually determine the sign of the slope. Since the values for y are increasing as the values for x are increasing, the slope is positive.

x y
0 4
-1 0

Use the grid to determine the slope.
How many units from 0 to -1? In what direction? 1 unit, positive. How many units from 4 to 0? In what direction? 4 units, negative.

equations image

Classroom Example 2

Determine the slope of the line in the graph below:

chart image

Answer:

Select any two points on the line, for example, (-8, 1) and (4, -2). Place the coordinates in the grid or formula to fine the slope.

x y
-8 1
4 -2

How many units from -8 to 4? In what direction? 12 units, positive.

How many units from 1 to -2? In what direction? 3 units, negative.

equation image

Using the formula for slope:

equation image
/instruction/clarification/mathematics/grade8/xml/1C2a.xml
Resources for Objective 1.C.2.a:
CLARIFICATIONS | Sample Assessments |