SOLUTION: The equation of the line that goes through the point (3,2) and is parallel to the line 2x+5y=3 is:

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Question 995718: The equation of the line that goes through the point (3,2) and is parallel to the line 2x+5y=3
is:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the line that goes through the point (3,2) and is parallel to the line 2x%2B5y=3=>y=-%282%2F5%29x%2B3%2F5

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%2F5 (its from the slope of y=%28-2%2F5%29%2Ax%2B3%2F5 which is also -2%2F5). Also since the unknown line goes through (3,2), 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-2=%28-2%2F5%29%2A%28x-3%29 Plug in m=-2%2F5, x%5B1%5D=3, and y%5B1%5D=2



y-2=%28-2%2F5%29%2Ax%2B%282%2F5%29%283%29 Distribute -2%2F5



y-2=%28-2%2F5%29%2Ax%2B6%2F5 Multiply



y=%28-2%2F5%29%2Ax%2B6%2F5%2B2Add 2 to both sides to isolate y

y=%28-2%2F5%29%2Ax%2B6%2F5%2B10%2F5 Make into equivalent fractions with equal denominators



y=%28-2%2F5%29%2Ax%2B16%2F5 Combine the fractions



y=%28-2%2F5%29%2Ax%2B16%2F5 Reduce any fractions

So the equation of the line that is parallel to y=%28-2%2F5%29%2Ax%2B3%2F5 and goes through (3,2) is y=%28-2%2F5%29%2Ax%2B16%2F5


So here are the graphs of the equations y=%28-2%2F5%29%2Ax%2B3%2F5 and y=%28-2%2F5%29%2Ax%2B16%2F5



graph of the given equation y=%28-2%2F5%29%2Ax%2B3%2F5 (red) and graph of the line y=%28-2%2F5%29%2Ax%2B16%2F5(green) that is parallel to the given graph and goes through (3,2)