SOLUTION: Find the equation of the line in slope-intercept form that is perpendicular to y = -1/4 x + 3 and passes through (3/2, 5).

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line in slope-intercept form that is perpendicular to y = -1/4 x + 3 and passes through (3/2, 5).      Log On


   

Question 705594: Find the equation of the line in slope-intercept form that is perpendicular to y = -1/4 x + 3 and passes through (3/2, 5).
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 1%2F4, 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%281%2F4%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%284%2F1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-4%2F1 Multiply the fractions.


So the perpendicular slope is -4



So now we know the slope of the unknown line is -4 (its the negative reciprocal of 1%2F4 from the line y=%281%2F4%29%2Ax%2B3). Also since the unknown line goes through (3/2,5), 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-5=-4%2A%28x-3%2F2%29 Plug in m=-4, x%5B1%5D=3%2F2, and y%5B1%5D=5



y-5=-4%2Ax%2B%284%29%283%2F2%29 Distribute -4



y-5=-4%2Ax%2B12%2F2 Multiply



y=-4%2Ax%2B12%2F2%2B5Add 5 to both sides to isolate y

y=-4%2Ax%2B12%2F2%2B10%2F2 Make into equivalent fractions with equal denominators



y=-4%2Ax%2B22%2F2 Combine the fractions



y=-4%2Ax%2B11 Reduce any fractions

So the equation of the line that is perpendicular to y=%281%2F4%29%2Ax%2B3 and goes through (3%2F2,5) is y=-4%2Ax%2B11


So here are the graphs of the equations y=%281%2F4%29%2Ax%2B3 and y=-4%2Ax%2B11




graph of the given equation y=%281%2F4%29%2Ax%2B3 (red) and graph of the line y=-4%2Ax%2B11(green) that is perpendicular to the given graph and goes through (3%2F2,5)