a line parallel to y = 6x + 7, will have the same exact slope, hmm what is the slope of y = 6x + 7 anyway? [tex]\bf y=6x+7\implies y=\stackrel{slope}{6}x+7[/tex]
so, what is the equation of a line whose slope is 6 and passes through (0, 9)?
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 0}}\quad ,&{{ 9}})\quad
% (c,d)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 6
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-9=6(x-0)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-9=6x\implies y=6x+9[/tex]
