SOLUTION: Parallel to x-y=4 and passing through (-3,2)

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Question 717587: Parallel to x-y=4 and passing through (-3,2)
Answer by MathLover1(20849) About Me  (Show Source):
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given:
the line is parallel to x-y=4 or y=x-4 and passing through (-3,2)
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 1 (its from the slope of y=1%2Ax-4 which is also 1). 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=1%2A%28x%2B3%29 Plug in m=1, x%5B1%5D=-3, and y%5B1%5D=2



y-2=1%2Ax-%281%29%28-3%29 Distribute 1



y-2=1%2Ax%2B3 Multiply



y=1%2Ax%2B3%2B2Add 2 to both sides to isolate y

y=1%2Ax%2B5 Combine like terms

So the equation of the line that is parallel to y=1%2Ax-4 and goes through (-3,2) is y=1%2Ax%2B5


So here are the graphs of the equations y=1%2Ax-4 and y=1%2Ax%2B5



graph of the given equation y=1%2Ax-4 (red) and graph of the line y=1%2Ax%2B5(green) that is parallel to the given graph and goes through (-3,2)