SOLUTION: Write an equation of the line that passes through (2,−5) and is parallel to the line 2y=3x+10.

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Question 999969: Write an equation of the line that passes through (2,−5) and is parallel to the line 2y=3x+10.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

an equation of the line that passes through (2,-5) and is parallel to the line 2y=3x%2B10 or y=%283%2F2%29x%2B5 will be:
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 1.5 (its from the slope of y=1.5%2Ax%2B5 which is also 1.5). Also since the unknown line goes through (2,-5), 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%2B5=1.5%2A%28x-2%29 Plug in m=1.5, x%5B1%5D=2, and y%5B1%5D=-5



y%2B5=1.5%2Ax-%281.5%29%282%29 Distribute 1.5



y%2B5=1.5%2Ax-3 Multiply



y=1.5%2Ax-3-5Subtract -5 from both sides to isolate y

y=1.5%2Ax-8 Combine like terms

So the equation of the line that is parallel to y=1.5%2Ax%2B5 and goes through (2,-5) is y=1.5%2Ax-8


So here are the graphs of the equations y=1.5%2Ax%2B5 and y=1.5%2Ax-8



graph of the given equation y=1.5%2Ax%2B5 (red) and graph of the line y=1.5%2Ax-8(green) that is parallel to the given graph and goes through (2,-5)