Question

Find the slope of g(x) with g(10)=52; g(6)=42

Answer 1

\(\bf g(10)=52\to
\begin{cases}
x=10\\
\bf y=52
\end{cases}\to (10,52)
\\ \quad \\
g(6)=42\to
\begin{cases}
x=6\\
\bf y=42
\end{cases}\to (6,42)
\\ \quad \\
\textit{so the line passes through }(10,52)\ and\ (6,42)
\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 10}}\quad ,&{\color{blue}{ 52}})\quad &({\color{red}{ 6}}\quad ,&{\color{blue}{ 42}})
\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}}}\)