SOLUTION: the line parallel to y=5x+1 that passes through (3,8).

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Question 918538: the line parallel to y=5x+1 that passes through (3,8).
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 5 (its from the slope of y=5%2Ax%2B1 which is also 5). Also since the unknown line goes through (3,8), 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-8=5%2A%28x-3%29 Plug in m=5, x%5B1%5D=3, and y%5B1%5D=8



y-8=5%2Ax-%285%29%283%29 Distribute 5



y-8=5%2Ax-15 Multiply



y=5%2Ax-15%2B8Add 8 to both sides to isolate y

y=5%2Ax-7 Combine like terms

So the equation of the line that is parallel to y=5%2Ax%2B1 and goes through (3,8) is y=5%2Ax-7


So here are the graphs of the equations y=5%2Ax%2B1 and y=5%2Ax-7



graph of the given equation y=5%2Ax%2B1 (red) and graph of the line y=5%2Ax-7(green) that is parallel to the given graph and goes through (3,8)