One of my teachers asked me to incorporate a different perspective on writing a line in slope-intercept form when given two points.  As I drafted notes, I thought, “Why not write the steps in my blog”.  I’ll have a hard copy of my notes and then I can share them with multiple people.  🙂

Part 1 – Exploring with Desmos

1. Go to Desmos.com.  Desmos provides a visual!  Our visual learners can glean more understanding of linear equations than expected if we incorporate interactive visual tools such as Desmos.
2. Click on Add item and select table
3.  
4. Give 2 points (2, -7) & (8, -4)
5. Ask students to enter in the points into the table
6. Ask them to state an observation for the slope
   1. Anticipating:  positive, less than 1
7. Ask them to state an observation for the y-intercept
   1. Anticipating:  a negative value
8. Ask students to press the button to connect the points.
9. Have them count the rise and run
   1. rise – 3, run = 6
   2. reduced = 1/2
10. Ask students to enter the equation y =  1/2x
11. Ask students to move the new line (red) so it covers the green segment.
    1. Eventually they’ll get y = 1/2x-8

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Part 2 – Using Formulas

1. Now that the students know the answer, they can use that answer to guide their calculations.
2. Use slope formula to calculate the rate of change
3. Substitute to solve for the y-intercept:  y = mx + b
   1. m = 1/2
   2. pick either point (2, -7) or (8, -4) to substitute into (x, y)

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Another problem

1. Points:  (-30, 9) & (-45, 18)
2. This problem has a trickier slope.
   1. In the graphic, you can see two forms of the equation. One reduce (red)  and the other not (orange).  This is a great situation to highlight when presented in class.  The orange line covering the red line proves that the 2 equations are equal.
3. Students, now must slide the line to match it with the green segment.
4. Repeat Part 2 – Using Formulas.