Slope and the Equation of a Line

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1. 1. The problem0:00
   Slope and the Equation of a Line

   through $(1, 2)$ and $(3, 8)$
2. 2. Slope0:09
   1. $$m = \frac{y_2 - y_1}{x_2 - x_1}$$
   2. $$m = \frac{8 - 2}{3 - 1} = \frac{6}{2} = 3$$
3. 3. Intercept0:19
   1. $$y = 3x + b$$
   2. $$2 = 3(1) + b$$
   3. $$b = -1$$
   4. $$y = 3x - 1$$
4. 4. See it on the graph0:35

5. 5. Recap0:46
   • ✓Slope $m = \dfrac{\Delta y}{\Delta x}$.
   • ✓Substitute one point to find $b$.
   • ✓Check with the other point: $3(3) - 1 = 8$.

Slope, slope-intercept and point-slope form, parallel and perpendicular lines.

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