Question

for a medal
A line passes through (2, –1) and (8, 4).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 2}}\quad ,&{\color{blue}{ -1}})\quad &({\color{red}{ 8}}\quad ,&{\color{blue}{ 4}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad
\begin{array}{llll}
a)\textit{ plug in the values} \\
b)\textit{move the "x" and "y" terms to the left-side}
\end{array}\\
\qquad \uparrow\\
\textit{point-slope form}\)