SOLUTION: find the equation of the line through(-5,8)and parallel to the line 4x+y=8

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Question 93845: find the equation of the line through(-5,8)and parallel to the line 4x+y=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First convert 4x+y=8 into slope intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


4x%2B1y=8 Start with the given equation


4x%2B1y-4x=8-4x Subtract 4x from both sides


1y=-4x%2B8 Simplify


The original equation 4x%2B1y=8 (standard form) is equivalent to y+=+-4x%2B8 (slope-intercept form)


The equation y+=+-4x%2B8 is in the form y=mx%2Bb where m=-4 is the slope and b=8 is the y intercept.





Now lets find the parallel line

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%2B8 which is also -4). Also since the unknown line goes through (-5,8), 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=-4%2A%28x%2B5%29 Plug in m=-4, x%5B1%5D=-5, and y%5B1%5D=8



y-8=-4%2Ax%2B%284%29%28-5%29 Distribute -4



y-8=-4%2Ax-20 Multiply



y=-4%2Ax-20%2B8Add 8 to both sides to isolate y

y=-4%2Ax-12 Combine like terms

So the equation of the line that is parallel to y=-4%2Ax%2B8 and goes through (-5,8) is y=-4%2Ax-12


So here are the graphs of the equations y=-4%2Ax%2B8 and y=-4%2Ax-12



graph of the given equation y=-4%2Ax%2B8 (red) and graph of the line y=-4%2Ax-12(green) that is parallel to the given graph and goes through (-5,8)