The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 4.6: Finding the Slope of a Line, Given Two

Points on the Line

Using a formula for finding the slope of a line is relatively easy, provided students understand the

formula. Most mistakes occur when students substitute incorrect values for the variables or make

errors in computation.

SPECIAL MATERIALS:

Graph paper, rulers

1. Ask your students to draw a straight line through points (1, 7) and (−1, 4) on graph paper.


2. Explain that they will use their graph to find the slope, or ‘‘steepness,’’ of the line through
   these points. Start with point (1, 7) and ask them how they can get to (−1, 4) by first moving
   vertically and then horizontally along the grid lines of the graph paper. (Move down 3 units
   and move 2 units to the left.) Remind your students that moving down is described as moving
   in a negative direction and moving to the left is also moving in a negative direction. The
   slope of the line through these points ishorizontal movementvertical movement which is equal to

− 3

− 2

or

3

2

.

3. Instruct your students to start with point (−1, 4) and ask them how they can get to (1, 7)
   using the same procedure. (Move up 3 units and move 2 units to the right.) Note that moving
   up is moving in a positive direction and moving right is also positive. Also note that the slope
   of the line is the same,

3

2

, regardless of the starting point.

4. Review the formula, information, and example on the worksheet with your students. Note
   that the example is completed in two different ways.

EXTRA HELP:

Using the formula is the most efficient way to find the slope of a line.

ANSWER KEY:

(1)− 4 (2)− 2 (3)

1

4

(4)

4

3

(5) 0

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(Challenge)Disagree. The correct slope is

4

3

. Dominic placed thex-values in the numerator
instead of the denominator.

148 THE ALGEBRA TEACHER’S GUIDE