Question

A student find the slope of the line between (8,17) and (1,4)

Answer 1

$\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{17})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-17}{1-8}\implies \cfrac{-13}{-7}\implies \cfrac{13}{7} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{17-4}{1-8}\stackrel{\leftarrow \textit{atop she used }y_1-y_2}{\frac{}{}}~\hfill$

Answer 2

For this case we have that by definition, the slope of a line is given by:

$m = \frac {y_ {2} -y_ {1}} {x_{2} -x_ {1}}$

According to the data we have the following points:

$(x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 8,17)$

Substituting we have:

$m = \frac {17-4} {8-1}\\m = \frac {13} {7}$

So, the slope is $\frac {13} {7}$

ANswer:

The student's mistake was to erroneously subtract the "x" coordinates from the points