Question

What is the slop of the line containing the points (4,-10 2/3), (-3,1)

Answer 1

let's firstly convert the mixed fraction to improper fraction.

`\bf \stackrel{mixed}{10(2)/(3)}\implies \cfrac{10\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{32}{3}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-(32)/(3)})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-\left( -(32)/(3) \right)}{-3-4}\implies \cfrac{1+(32)/(3)}{-7}\implies \cfrac{(3+32)/(3)}{-7}`

`\bf \cfrac{~~(35)/(3)~~}{(-7)/(1)} \implies \cfrac{\stackrel{5}{~~\begin{matrix} 35 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}~~}{3}\cdot \cfrac{1}{~~\begin{matrix} -7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{5}{3}`