SOLUTION: Please Help I am not sure how to do this problem L has y-intercept (0, _3) and is parallel to the line with equation y= -2/3+1

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Question 90103: Please Help I am not sure how to do this problem
L has y-intercept (0, _3) and is parallel to the line with equation y= -2/3+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is -2%2F3 (its from the slope of y=%28-2%2F3%29%2Ax%2B1 which is also -2%2F3). Also since the unknown line goes through (0,3), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-3=%28-2%2F3%29%2A%28x-0%29 Plug in m=-2%2F3, x%5B1%5D=0, and y%5B1%5D=3



y-3=%28-2%2F3%29%2Ax%2B%282%2F3%29%280%29 Distribute -2%2F3



y-3=%28-2%2F3%29%2Ax-0%2F3 Multiply



y=%28-2%2F3%29%2Ax-0%2F3%2B3Add 3 to both sides to isolate y

y=%28-2%2F3%29%2Ax-0%2F3%2B9%2F3 Make into equivalent fractions with equal denominators



y=%28-2%2F3%29%2Ax%2B9%2F3 Combine the fractions



y=%28-2%2F3%29%2Ax%2B3 Reduce any fractions

So the equation of the line that is parallel to y=%28-2%2F3%29%2Ax%2B1 and goes through (0,3) is y=%28-2%2F3%29%2Ax%2B3


So here are the graphs of the equations y=%28-2%2F3%29%2Ax%2B1 and y=%28-2%2F3%29%2Ax%2B3



graph of the given equation y=%28-2%2F3%29%2Ax%2B1 (red) and graph of the line y=%28-2%2F3%29%2Ax%2B3(green) that is parallel to the given graph and goes through (0,3)