Question 69046
write an equation in standard form of the line that has y-intercept=-4 and passes through (5,-3)
There are a couple of ways to do this.  One way is to use the slope intercept form of a line, {{{highlight(y=mx+b)}}}, where m=slope and b=y-intercept.
Let x=5, y=-3 and b=-4 and solve for m.
{{{-3=m(5)+(-4)}}}
{{{-3=5m-4}}}
{{{-3+4=5m-4+4}}}
{{{1=5m}}}
{{{1/5=5m/5}}}
{{{1/5=m}}}
Let m=1/5 and b=-4 and you have the slope intercept form of a line.
{{{y=(1/5)x+(-4)}}}
{{{y=(1/5)x-4}}}
The standard form of a line is {{{highlight(Ax+By=C)}}}, where A,B, and C are integers.  Some books also require that A is positive:
{{{5y=5(1/5)x+5(-4)}}}
{{{5y=x-20}}}
{{{-x+5y=x-x-20}}}
{{{-x+5y=-20}}}
{{{-1(-x)-1(5y)=-1(-20)}}}
{{{highlight(x-5y=20)}}}
Happy Calculating!!!!