SOLUTION: write the equation for the line that contains point(-4,2)and is parallel to the line 5x+y=8

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Question 449270: write the equation for the line that contains point(-4,2)and is parallel to the line 5x+y=8
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
point(-4,2)
the line 5x%2By=8...or ...y=-5x%2B8

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%2B8 which is also -5). Also since the unknown line goes through (-4,2), 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=-5%2A%28x%2B4%29 Plug in m=-5, x%5B1%5D=-4, and y%5B1%5D=2



y-2=-5%2Ax%2B%285%29%28-4%29 Distribute -5



y-2=-5%2Ax-20 Multiply



y=-5%2Ax-20%2B2Add 2 to both sides to isolate y

y=-5%2Ax-18 Combine like terms

So the equation of the line that is parallel to y=-5%2Ax%2B8 and goes through (-4,2) is y=-5%2Ax-18


So here are the graphs of the equations y=-5%2Ax%2B8 and y=-5%2Ax-18



graph of the given equation y=-5%2Ax%2B8 (red) and graph of the line y=-5%2Ax-18(green) that is parallel to the given graph and goes through (-4,2)