Question 11793
Your first step is correct.  You need to take the given equation of the line in standard form, and convert it to slope-intercept form, in order to find the slope of the given line.


7x-6y=-1
7x-6y=-1
-6y=-7x-1
y=7/6x+6


According to this, the slope of the given line is {{{m=7/6}}}, so the slope of the line parallel to this line is ALSO {{{7/6}}}.


There are two ways to go from here.  I recommend using the simplest formula you can here (y=mx+b), and substitute in the values that you know: m={{{7/6}}}, and x=-5 and y = -3, and solve for b.

y = mx + b
{{{ (-3) = (7/6)*(-5) + b}}}


To clear the ugly fraction, it's nice to multiply both sides by 6:
{{{6*(-3) = 6*(7/6)*(-5) + 6*b}}}  Divide out the 6 on the right side of the equation:
{{{-18 = -35 + 6b}}}


Add + 35 to each side:
{{{-18 + 35 = -35 + 35 + 6b}}}
{{{17 = 6b}}}


Divide both sides by 6:

{{{b= 17/6}}}  


Remember what b represents?  The y-intercept, so the final answer is:
{{{y = (7/6)*x + 17/6}}}


As a check, let x =  -5, substitute into this equation, and see if you get y = -3:

{{{y = (7/6)*x + 17/6}}}
{{{y = (7/6)*(-5) + 17/6}}}
{{{y = (-35)/6 + 17/6 }}} = {{{(-18)/6}}}= {{{-3}}}
It checks.


This may not be the most common method to solve this, but I think it's the easiest method!


R^2 at SCC