SOLUTION: please help me slove this equation: passes through (2,-3) and is parallel to the line y=-2/3x+1

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Question 501955: please help me slove this equation: passes through (2,-3) and is parallel to the line y=-2/3x+1
Answer by MathLover1(20849) 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 (2,-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%2B3=%28-2%2F3%29%2A%28x-2%29 Plug in m=-2%2F3, x%5B1%5D=2, and y%5B1%5D=-3



y%2B3=%28-2%2F3%29%2Ax%2B%282%2F3%29%282%29 Distribute -2%2F3



y%2B3=%28-2%2F3%29%2Ax%2B4%2F3 Multiply



y=%28-2%2F3%29%2Ax%2B4%2F3-3Subtract -3 from both sides to isolate y

y=%28-2%2F3%29%2Ax%2B4%2F3-9%2F3 Make into equivalent fractions with equal denominators



y=%28-2%2F3%29%2Ax-5%2F3 Combine the fractions



y=%28-2%2F3%29%2Ax-5%2F3 Reduce any fractions

So the equation of the line that is parallel to y=%28-2%2F3%29%2Ax%2B1 and goes through (2,-3) is y=%28-2%2F3%29%2Ax-5%2F3


So here are the graphs of the equations y=%28-2%2F3%29%2Ax%2B1 and y=%28-2%2F3%29%2Ax-5%2F3



graph of the given equation y=%28-2%2F3%29%2Ax%2B1 (red) and graph of the line y=%28-2%2F3%29%2Ax-5%2F3(green) that is parallel to the given graph and goes through (2,-3)