SOLUTION: Another slope that I have trouble with. CAn anyone give me a hand? Thanks! Write the equation of the line that passes through (0,3) and is parallel to 3y = x +10. Thanks

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Question 60982This question is from textbook college algebra
: Another slope that I have trouble with. CAn anyone give me a hand? Thanks!
Write the equation of the line that passes through (0,3) and is parallel to
3y = x +10.
Thanks again for your efforts! This question is from textbook college algebra

Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
The line has equation 3y+=+x%2B10
You want to get the line into a form y+=+mx%2Bb where x is the slope and b is the place on the y-axis where the line crosses the y-axis.
Divide both sides of the equation by 3 and you get
y+=+%281%2F3%29x%2B%2810%2F3%29
So, the slope of the line is 1%2F3.
Any line parallel to this line will also have a slope of 1%2F3.
So, we're looking for a line with equation y+=+%281%2F3%29x+%2B+b and we need to figure out what b is.
We know that point (0,3) is on the parallel line so we know that when x+=+0 then y+=+3. So, solve for b:
3+=+%281%2F3%29%2A0+%2B+b or 3+=+b.
So, the equation of the parallel line is y+=+%281%2F3%29x+%2B3.