Question

What is the equation in standard form of the line which passes through (4, –2) and has a slope of –3?

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ 4}}\quad ,&{\color{blue}{ 2}})\quad

\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies -3
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and move everything to the left}\\
\qquad \uparrow\\
\textit{point-slope form}\)