Question

Part II: Use the formula from Part I to find the slope of the line that goes through

each pair of point
A. (5, 7) and (-4,-2)
B. (1, 3) and (1,-10)

Answer 1

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{5}}} \implies \cfrac{ -9 }{ -9 } \implies 1 \\\\[-0.35em] ~\dotfill`

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-10}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ 0 } \implies unde fined`

something noteworthy, the second one has two points with the same x-coordinate, that means is a vertical line and all vertical lines have an undefined slope.