SOLUTION: will you please explain to me how to do this using an equation. i am so lost. It says, find the equation of the line that is perpendicular to -2x+7y=13 and passes through the poi

Algebra ->  Linear-equations -> SOLUTION: will you please explain to me how to do this using an equation. i am so lost. It says, find the equation of the line that is perpendicular to -2x+7y=13 and passes through the poi      Log On


   

Question 93773: will you please explain to me how to do this using an equation. i am so lost.
It says, find the equation of the line that is perpendicular to -2x+7y=13 and passes through the point (6,0)
If you could help me, that would be wonderful. thank you and God bless.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First convert -2x+7y=13 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)


-2x%2B7y=13 Start with the given equation


-2x%2B7y%2B2x=13%2B2x Add 2x to both sides


7y=2x%2B13 Simplify


%287y%29%2F%287%29=%282x%2B13%29%2F%287%29 Divide both sides by 7 to isolate y


y+=+%282x%29%2F%287%29%2B%2813%29%2F%287%29 Break up the fraction on the right hand side


y+=+%282%2F7%29x%2B13%2F7 Reduce and simplify


The original equation -2x%2B7y=13 (standard form) is equivalent to y+=+%282%2F7%29x%2B13%2F7 (slope-intercept form)


The equation y+=+%282%2F7%29x%2B13%2F7 is in the form y=mx%2Bb where m=2%2F7 is the slope and b=13%2F7 is the y intercept.





Now lets find the equation of the perpendicular line
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 2%2F7, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%282%2F7%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%287%2F2%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-7%2F2 Multiply the fractions.


So the perpendicular slope is -7%2F2



So now we know the slope of the unknown line is -7%2F2 (its the negative reciprocal of 2%2F7 from the line y=%282%2F7%29%2Ax%2B13%2F7). Also since the unknown line goes through (6,0), 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-0=%28-7%2F2%29%2A%28x-6%29 Plug in m=-7%2F2, x%5B1%5D=6, and y%5B1%5D=0



y-0=%28-7%2F2%29%2Ax%2B%287%2F2%29%286%29 Distribute -7%2F2



y-0=%28-7%2F2%29%2Ax%2B42%2F2 Multiply



y=%28-7%2F2%29%2Ax%2B42%2F2%2B0Add 0 to both sides to isolate y

y=%28-7%2F2%29%2Ax%2B42%2F2%2B0%2F2 Make into equivalent fractions with equal denominators



y=%28-7%2F2%29%2Ax%2B42%2F2 Combine the fractions



y=%28-7%2F2%29%2Ax%2B21 Reduce any fractions

So the equation of the line that is perpendicular to y=%282%2F7%29%2Ax%2B13%2F7 and goes through (6,0) is y=%28-7%2F2%29%2Ax%2B21


So here are the graphs of the equations y=%282%2F7%29%2Ax%2B13%2F7 and y=%28-7%2F2%29%2Ax%2B21




graph of the given equation y=%282%2F7%29%2Ax%2B13%2F7 (red) and graph of the line y=%28-7%2F2%29%2Ax%2B21(green) that is perpendicular to the given graph and goes through (6,0)