[tex]\bf \begin{array}{ccllll}
\begin{array}{cllll}
HCF\\
x
\end{array} &
\begin{array}{cllll}
\$\\
y
\end{array}\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
19&31.91\\
47&69.71
\end{array}\\\\
-----------------------------\\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 19}}\quad ,&{{ 31.91}})\quad
% (c,d)
&({{ 47}}\quad ,&{{ 69.71}})
\end{array}[/tex]
[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{69.71-31.91}{47-19}
\\\\\\
m=\cfrac{rise}{run}\implies \cfrac{37.8}{26}\iff \cfrac{189}{130}
\\\\\\
\textit{now, what if HCF is 35? HCF is "x" or the "run"}
\\\\\\
\cfrac{rise}{run}\qquad \cfrac{rise}{35}=\cfrac{189}{130}\implies rise=\cfrac{35\cdot 189}{130}[/tex]
