SOLUTION: Write an equation of the line containing the given point and perpendicular to the given line. Express in the form y= m x + b (7,8) ; 5x + y = 7 The equation of the line is y

Algebra ->  Coordinate-system -> SOLUTION: Write an equation of the line containing the given point and perpendicular to the given line. Express in the form y= m x + b (7,8) ; 5x + y = 7 The equation of the line is y       Log On


   

Question 237339: Write an equation of the line containing the given point and perpendicular to the given line. Express in the form y= m x + b
(7,8) ; 5x + y = 7
The equation of the line is y =
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5x+%2B+y+=+7 Start with the given equation


y+=+-5x%2B7 Subtract 5x from both sides.


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 -5, 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%28-5%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-5%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=1%2F5 Multiply the fractions.


So the perpendicular slope is 1%2F5



So now we know the slope of the unknown line is 1%2F5 (its the negative reciprocal of -5 from the line y=-5%2Ax%2B7). Also since the unknown line goes through (7,8), 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=%281%2F5%29%2A%28x-7%29 Plug in m=1%2F5, x%5B1%5D=7, and y%5B1%5D=8



y-8=%281%2F5%29%2Ax-%281%2F5%29%287%29 Distribute 1%2F5



y-8=%281%2F5%29%2Ax-7%2F5 Multiply



y=%281%2F5%29%2Ax-7%2F5%2B8Add 8 to both sides to isolate y

y=%281%2F5%29%2Ax-7%2F5%2B40%2F5 Make into equivalent fractions with equal denominators



y=%281%2F5%29%2Ax%2B33%2F5 Combine the fractions



y=%281%2F5%29%2Ax%2B33%2F5 Reduce any fractions

So the equation of the line that is perpendicular to y=-5%2Ax%2B7 and goes through (7,8) is y=%281%2F5%29%2Ax%2B33%2F5


So here are the graphs of the equations y=-5%2Ax%2B7 and y=%281%2F5%29%2Ax%2B33%2F5




graph of the given equation y=-5%2Ax%2B7 (red) and graph of the line y=%281%2F5%29%2Ax%2B33%2F5(green) that is perpendicular to the given graph and goes through (7,8)