Question 54879
write an equation in slope intercept form for the line that satisfies each set of conditions.
passes through (4,6) parallel to the graph of Y=2/3x+5
The line you're given is in slope intercept form: {{{highlight(y=mx+b)}}} where m=slope and (0,b)=y-intercept.
{{{y=highlight(2/3)x+5}}}  it's slope m=2/3.
Parallel lines have the same slope, so you need and equation of a line with a slope m=2/3 going through (x1,y1)=(4,6)
When you have a point and a slope and need the equation of a line you use the point slope formula: {{{highlight(y-y1=m(x-x1))}}}, where m=slope and (x1,y1) is the point you're going through.
your m=2/3 and (x1,y1)=(4,6)
{{{y-6=(2/3)(x-4)}}}
{{{3(y-6)=3(2/3)(x-4)}}}
{{{3y-18=(6/3)(x-4)}}}
{{{3y-18=2(x-4)}}}
{{{3y-18=2x-8}}}
{{{3y-18+18=2x-8+18}}}
{{{3y=2x+10}}}
{{{3y/3=2x/3+10/3}}}
{{{highlight(y=(2/3)x+10/3)}}}
Happy Calculating!!!