Question

Find a point-slope form equation for the line through the point (-4, 3) with a slope of -2/3.

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({\color{red}{ -4}}\quad ,&{\color{blue}{ 3}})\quad
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies-\cfrac{2}{3}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 2

y-3=-2/3(x+4)
is that correct ?

Answer 3

yeap, that's correct :)