Question

A line that includes the points (-6,-5) and (j,4) has an undefined slope. What is the value of j?

Answer 1

if we have an undefined line, that simply means the fraction form of the slope has a 0 at the bottom, namely  

$\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{}{\underset{\underset{here}{\uparrow}}{0}}$

therefore then

$\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{j}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-5)}{j-(-6)}\implies \cfrac{4+5}{j+6}\implies \stackrel{\stackrel{und efined}{\downarrow }}{\cfrac{~~~~}{0}} \\\\\\ \stackrel{\textit{therefore thus}}{j+6=0}\implies j=-6$