SOLUTION: parallel to the graph 3x+2y=5 and y-intercept(0,-1)

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Question 764087: parallel to the graph 3x+2y=5 and y-intercept(0,-1)
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
parallel to the graph 3x+2y=5 and y-intercept(0,-1)
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Rearrange the equation:
y = (-3/2)x + (5/2)
------
slope of the parallel line is -3/2
y-intercept is(0,-1)
--------
Equation:
y = (-3/2)x - 1
========================================
Cheers,
Stan H.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2B2y=5
2y=-3x%2B5
y=-%283%2F2%29x%2B5%2F2
y-intercept (0,-1)

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 -3%2F2 (its from the slope of y=%28-3%2F2%29%2Ax%2B5%2F2 which is also -3%2F2). Also since the unknown line goes through (0,-1), 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%2B1=%28-3%2F2%29%2A%28x-0%29 Plug in m=-3%2F2, x%5B1%5D=0, and y%5B1%5D=-1



y%2B1=%28-3%2F2%29%2Ax%2B%283%2F2%29%280%29 Distribute -3%2F2



y%2B1=%28-3%2F2%29%2Ax-0%2F2 Multiply



y=%28-3%2F2%29%2Ax-0%2F2-1Subtract -1 from both sides to isolate y

y=%28-3%2F2%29%2Ax-0%2F2-2%2F2 Make into equivalent fractions with equal denominators



y=%28-3%2F2%29%2Ax-2%2F2 Combine the fractions



y=%28-3%2F2%29%2Ax-1 Reduce any fractions

So the equation of the line that is parallel to y=%28-3%2F2%29%2Ax%2B5%2F2 and goes through (0,-1) is y=%28-3%2F2%29%2Ax-1


So here are the graphs of the equations y=%28-3%2F2%29%2Ax%2B5%2F2 and y=%28-3%2F2%29%2Ax-1



graph of the given equation y=%28-3%2F2%29%2Ax%2B5%2F2 (red) and graph of the line y=%28-3%2F2%29%2Ax-1(green) that is parallel to the given graph and goes through (0,-1)