Question

Find the equation for the line passing through the point (−1,1) ( − 1 , 1 ) and parallel to the line whose equation is y=2x+12.

Answer 1

So, parallel lines have the same slope, therefore a parallel line to 2x+12, will have the same slope as that one, so which is it?   $\bf y=\stackrel{slope}{2}x\stackrel{y-intercept}{+12}$

so, we're really looking for the equation of a line whose slope is 2, and runs through -1,1.

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -1}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 2 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2[x-(-1)] \\\\\\ y-1=2(x+1)\implies y-1=2x+2\implies y=2x+3$