Writing Linear Equations in Point-Slope Form

Our equation is written in point-slope form. $\begin{gathered} y-y_1=m(x-x_1) \end{gathered}$ Here, $m$ is the slope and $(x_1,y_1)$ is a point on the line. Let's rewrite the given equation to match the above format. $\begin{aligned} y+10= \dfrac{5}{6}(x-2)\quad\Leftrightarrow\quad y-(\text{-}10)= \dfrac{5}{6}(x-2) \end{aligned}$ Now, we can identify the slope, $m,$ and one of the points. $\begin{aligned} \textbf{Slope: }& \ \ m=\dfrac{5}{6}\\ \textbf{Point: }& \ \ (2,\text{-}10) \end{aligned}$

$\begin{aligned} y-\dfrac{3}{4}= \text{-}2(x+1)\quad\Leftrightarrow\quad y-\dfrac{3}{4}= \text{-}2(x-(\text{-}1)) \end{aligned}$ We can now identify the slope as $m=\text{-}2$ and one point as $\left(\text{-}1,\frac{3}{4}\right).$