SOLUTION: Write an equation of the line in slope-intercept form that passes through (5,3) and is perpendicular to y=-5x+3

Algebra ->  Linear-equations -> SOLUTION: Write an equation of the line in slope-intercept form that passes through (5,3) and is perpendicular to y=-5x+3      Log On


   

Question 938292: Write an equation of the line in slope-intercept form that passes through (5,3) and is perpendicular to y=-5x+3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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%2B3). Also since the unknown line goes through (5,3), 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-3=%281%2F5%29%2A%28x-5%29 Plug in m=1%2F5, x%5B1%5D=5, and y%5B1%5D=3



y-3=%281%2F5%29%2Ax-%281%2F5%29%285%29 Distribute 1%2F5



y-3=%281%2F5%29%2Ax-5%2F5 Multiply



y=%281%2F5%29%2Ax-5%2F5%2B3Add 3 to both sides to isolate y

y=%281%2F5%29%2Ax-5%2F5%2B15%2F5 Make into equivalent fractions with equal denominators



y=%281%2F5%29%2Ax%2B10%2F5 Combine the fractions



y=%281%2F5%29%2Ax%2B2 Reduce any fractions

So the equation of the line that is perpendicular to y=-5%2Ax%2B3 and goes through (5,3) is y=%281%2F5%29%2Ax%2B2


So here are the graphs of the equations y=-5%2Ax%2B3 and y=%281%2F5%29%2Ax%2B2




graph of the given equation y=-5%2Ax%2B3 (red) and graph of the line y=%281%2F5%29%2Ax%2B2(green) that is perpendicular to the given graph and goes through (5,3)