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**

- 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.
- Click on Add item and select table
- Give 2 points (2, -7) & (8, -4)
- Ask students to enter in the points into the table
- Ask them to state an observation for the slope
- Anticipating: positive, less than 1

- Ask them to state an observation for the y-intercept
- Anticipating: a negative value

- Ask students to press the button to connect the points.
- Have them count the rise and run
- rise – 3, run = 6
- reduced = 1/2

- Ask students to enter the equation y = 1/2x
- Ask students to move the new line (red) so it covers the green segment.
- Eventually they’ll get y = 1/2x-8

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**Part 2 – Using Formulas**

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

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**Another problem**

- Points: (-30, 9) & (-45, 18)
- This problem has a trickier slope.
- 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.

- Students, now must slide the line to match it with the green segment.
- Repeat Part 2 – Using Formulas.