Question 115946
This is a point-slope problem.  You are given a point, and enough information to determine the slope, because you are given a parallel line and we know that the slopes of parallel lines are equal.


{{{2x+3y=-1}}}  In order to find the slope of a line, solve the equation for y which puts the equation into slope-intercept form {{{y=mx+b}}} where m is the slope and b is the y-intercept.


{{{3y=-2x-1}}}
{{{y=((-2)/3)x-1/3}}}.  so now we know that the slope of the line we are trying to define is {{{((-2)/3)}}}


Knowing a point on the line and the slope, we can now use the point-slope form of the line {{{(y-y[1])=m(x-x[1])}}} to write the equation directly.


{{{y-(-5)=((-2)/3)(x-(-4))}}} is the equation of the specified line, but it needs to be simplified


{{{y+5=(-2/3)(x+4)}}}


Now, you can put it into standard form {{{ax+by=c}}}:


{{{3y+15=-2x-8}}}
{{{2x+3y=-23}}}


Or, you could put it into slope-intercept form {{{y=mx+b}}}


{{{y=(-2/3)x-(23/3)}}}


Notice that the standard form differs from the given equation only in the constant term.  This should give you a clue to the relationship between the coefficients on the x and y terms in a standard form equation and the slope of the line.


{{{graph(600,600,-10,10,-10,10,(-2/3)x-(1/3),(-2/3)x-(23/3))}}}