Question

Write an equation that meets the given conditions?
A line that passes through the points (2,7) and (6,15)
A line that passes through (2,1) and (6,9)

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 7}})\quad &({\color{red}{ 6}}\quad ,&{\color{blue}{ 15}})\\
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 1}})\quad &({\color{red}{ 6}}\quad ,&{\color{blue}{ 9}})
\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-y_1={\color{green} m}(x-x_1)\qquad \textit{plug in your values and solve for "y"}\\
\qquad \uparrow \\
\textit{point-slope form}\)

Answer 2

alternatively,

y = mx + b

substitute your known x, y values to find m and b