part I
[tex]\bf \begin{array}{l|lllllll}
x&2&\boxed{4}&6&8&\boxed{10}&12&14\\\\
y&1&\boxed{6}&11&16&\boxed{21}&26&31
\end{array}\implies
\begin{array}{llll}
(4,6)\\\\
(10,21)
\end{array}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 4}}\quad ,&{{ 6}})\quad
% (c,d)
&({{ 10}}\quad ,&{{ 21}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{21-6}{10-4}[/tex]
part II
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad
\begin{array}{llll}
\textit{plug in the values for }
\begin{cases}
y_1=6\\
x_1=4\\
m=\boxed{?}
\end{cases}\\
\end{array}\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}[/tex]
now, the form above is the point-slope form, and that'd be the equation, you can leave it like so, or you can solve for "y", and put it in slope-intercept, same equation though.
