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Farid Movsumov · Answer 1 · 2018-01-14T08:04:14+0000

a line parallel to y = 6x + 7, will have the same exact slope, hmm what is the slope of y = 6x + 7 anyway?
$\bf y=6x+7\implies y=\stackrel{slope}{6}x+7$

so, what is the equation of a line whose slope is 6 and passes through (0, 9)?

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 0}}\quad ,&{{ 9}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 6 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-9=6(x-0)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-9=6x\implies y=6x+9$

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