SOLUTION: Write an equation of the line that is parallel to the given line y = 2x + 3 and the given point (-4,1).

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Question 700972: Write an equation of the line that is parallel to the given line
y = 2x + 3 and the given point (-4,1).
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 2 (its from the slope of y=2%2Ax%2B3 which is also 2). Also since the unknown line goes through (-4,1), 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-1=2%2A%28x%2B4%29 Plug in m=2, x%5B1%5D=-4, and y%5B1%5D=1



y-1=2%2Ax-%282%29%28-4%29 Distribute 2



y-1=2%2Ax%2B8 Multiply



y=2%2Ax%2B8%2B1Add 1 to both sides to isolate y

y=2%2Ax%2B9 Combine like terms

So the equation of the line that is parallel to y=2%2Ax%2B3 and goes through (-4,1) is y=2%2Ax%2B9


So here are the graphs of the equations y=2%2Ax%2B3 and y=2%2Ax%2B9



graph of the given equation y=2%2Ax%2B3 (red) and graph of the line y=2%2Ax%2B9(green) that is parallel to the given graph and goes through (-4,1)