1: How to Successfully Explain the Slope Formula

Understanding values representing the x and y values is critical for the correct placement of the x and y values in the slope formula.

This may present a challenge to some students. For example:

As students view two ordered pairs, it is important that they can clearly visualize which values represent x and which ones represent y.

Next, when plugging the x and y values into the formula it is important to copy the correct x and y values to the appropriate section of the formula. If the identification of the x and y values of the ordered pair are incorrectly identified, the order in which they are plugged into the formula will also be incorrect.

• A.  Use color–coding for the x and y values concepts. 
  

   My preference is to use red for the x values and green for the y values. Red and green are contrasting colors, which helps students to visually distinguish between x and y values. 

  
  

  If the ordered pairs found on a worksheet are not color-coded, students may color-code the x and y values with highlighters or circling values in the chosen color.

  
  

   It is also ideal to continue to use these same colors for other graphing purposes, as it provides students with visual memory connections and associations. 

  
  

  B.  Students may use the index and middle fingers of their opposite writing hand to point to both x values within the two ordered pairs while copying these values into the slope formula.  Next, students repeat the process to copy the y values.

  
  

  C.  For some students, covering up the values of the variable, x or y may also be helpful as it visually cancels out the other values in the ordered pair.  

  
  

  D.  Provide larger images of ordered pairs.

Before further explaining the slope formula, students will do best if they are confident plotting points of ordered pairs and naming ordered pairs of points on the Cartesian Plane.

When reviewing values of ordered pairs, use an illustration of a line with points.

Explain the following:
A point on a line is made up of an x and y value.
The x and y value represent an ordered pair or coordinate, such as (-2, -1).
It is an ordered pair because the points are represented in alphabetical order, the x value followed by the y value.
The coordinate describes the location of the point on the x/y coordinate plane.

To further help students make connections with these terms, I mention a game that use coordinates. Sometimes I even have the students play the game, though modify the values for the coordinates with an x and y axis and include numbers as found on the Cartesian Plane.

When explaining these terms, it is helpful to have a graph with a line and listed ordered pairs. See the example below.

Continue to refer to a line and its points on the graph while discussing the formula for slope.

Though the process might appear long and drawn out, it is worth the time to help students get it right the first time. Also, emphasize the importance of completing steps. Over time, some students may be able to skip some of the steps illustrated. Others will need to continue to show steps, particularly those students who are overwhelmed with thinking about too much at a time.

Students experience success using the slope formula when provided a review of the points on the line, ordered pairs, and subscripts prior to instruction of the slope formula.