SOLUTION: What is the slope intercept equation of the line parallel to {{{4x-y=3}}} passing through the point "(2,7)"

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Question 662219: What is the slope intercept equation of the line parallel to 4x-y=3 passing through the point "(2,7)"
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4x-y=3 passing through the point "(2,7)"
4x-3=y


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 (its from the slope of y=4%2Ax-3 which is also 4). Also since the unknown line goes through (2,7), 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-7=4%2A%28x-2%29 Plug in m=4, x%5B1%5D=2, and y%5B1%5D=7



y-7=4%2Ax-%284%29%282%29 Distribute 4



y-7=4%2Ax-8 Multiply



y=4%2Ax-8%2B7Add 7 to both sides to isolate y

y=4%2Ax-1 Combine like terms

So the equation of the line that is parallel to y=4%2Ax-3 and goes through (2,7) is y=4%2Ax-1


So here are the graphs of the equations y=4%2Ax-3 and y=4%2Ax-1



graph of the given equation y=4%2Ax-3 (red) and graph of the line y=4%2Ax-1(green) that is parallel to the given graph and goes through (2,7)