SOLUTION: which line is parallel to the line whose equation is 4x +3y=7 and also pass through the point(-5,2)?

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Question 696953: which line is parallel to the line whose equation is 4x
+3y=7 and also pass through the point(-5,2)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
4x%2B3y=7...=>...3y=-4x%2B7...=>...y=-%284%2F3%29x%2B7%2F3
and also pass through the point(-5,2)

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 -4%2F3 (its from the slope of y=%28-4%2F3%29%2Ax%2B7%2F3 which is also -4%2F3). Also since the unknown line goes through (-5,2), 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=%28-4%2F3%29%2A%28x%2B5%29 Plug in m=-4%2F3, x%5B1%5D=-5, and y%5B1%5D=2



y-2=%28-4%2F3%29%2Ax%2B%284%2F3%29%28-5%29 Distribute -4%2F3



y-2=%28-4%2F3%29%2Ax-20%2F3 Multiply



y=%28-4%2F3%29%2Ax-20%2F3%2B2Add 2 to both sides to isolate y

y=%28-4%2F3%29%2Ax-20%2F3%2B6%2F3 Make into equivalent fractions with equal denominators



y=%28-4%2F3%29%2Ax-14%2F3 Combine the fractions



y=%28-4%2F3%29%2Ax-14%2F3 Reduce any fractions

So the equation of the line that is parallel to y=%28-4%2F3%29%2Ax%2B7%2F3 and goes through (-5,2) is y=%28-4%2F3%29%2Ax-14%2F3


So here are the graphs of the equations y=%28-4%2F3%29%2Ax%2B7%2F3 and y=%28-4%2F3%29%2Ax-14%2F3



graph of the given equation y=%28-4%2F3%29%2Ax%2B7%2F3 (red) and graph of the line y=%28-4%2F3%29%2Ax-14%2F3(green) that is parallel to the given graph and goes through (-5,2)