Question 74978
Find the standard form for the equation of the line which passes through the point (-1,-2) and is parallel to the line whose equation is 6x+2y=4? 
Parallel lines have equal slopes, so our line has the same slope as 6x+2y=4.
To find the slope of the equation of a line, put the line in slope-intercept form: {{{highlight(y=mx+b)}}}, where m=slope and (0,b)=y-intercept
{{{6x+2y=4}}}
{{{6x-6x+2y=-6x+4}}}
{{{2y=-6x+4}}}
{{{2y/2=-6x/2+4/2}}}
{{{y=-3x+2}}}  The slope is, m=-3
Therefore, our line has a slope of m=-3 and goes through the point (-1,-2).
Some teachers use the slope intercept form of a line to find b and make the equation.
Others use the point-slope formula (my preference): {{{highlight(y-y[1]=m(x-x[1]))}}}, where m=slope and (x1,y1)=given point.
(x1,y1)=(-1,-2) and m=-3
{{{y-(-2)=-3(x-(-1))}}}
{{{y+2=-3(x+1)}}}
{{{y+2=-3x-3}}}
The standard form of a line is {{{highlight(Ax+B=C)}}}, where A,B, and C are integers and most books and teachers prefer that A be positive.
{{{3x+y+2=3x-3x-3}}}
{{{3x+y+2=-3}}}
{{{3x+y+2-2=-3-2}}}
{{{highlight(3x+y=-5)}}}
Happy Calculating!!!!