well, for a function, in a set of x,y ordered pairs, so long the "x" are not repeated, then it IS a function, let's look
[tex]\bf \{(\boxed{0},-7), (\boxed{1},-4), (\boxed{2},-1), (\boxed{-1},-10)\}\impliedby
\begin{array}{llll}
\textit{nope, no x-re} peats\\
\textit{it is indeed a}\\
function
\end{array}[/tex]
so then, let's use two of those points ahemm let's see say (0, -7) and (2, -1)
so, what's the equation of a line that goes through (0, -7) and (2, -1)?
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 0}}\quad ,&{{ -7}})\quad
% (c,d)
&({{ 2}}\quad ,&{{ -1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-1-(-7)}{2-0}\implies \cfrac{-1+7}{2-0}
\\\\\\
\cfrac{6}{2}\implies 3
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-7)=3(x-0)\implies y+7=3x
\\\\\\
y=3x-7[/tex]
