SOLUTION: Write an equation in slope-intercept form for the line that satisfies each set of conditions. passes through (2,-5), perpindicular to the graph of y=1/4x +7

Algebra ->  Linear-equations -> SOLUTION: Write an equation in slope-intercept form for the line that satisfies each set of conditions. passes through (2,-5), perpindicular to the graph of y=1/4x +7      Log On


   

Question 104645: Write an equation in slope-intercept form for the line that satisfies each set of conditions.
passes through (2,-5), perpindicular to the graph of y=1/4x +7
Answer by jim_thompson5910(35256) 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%2B7). Also since the unknown line goes through (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%2B5=-4%2A%28x-2%29 Plug in m=-4, x%5B1%5D=2, and y%5B1%5D=-5



y%2B5=-4%2Ax%2B%284%29%282%29 Distribute -4



y%2B5=-4%2Ax%2B8 Multiply



y=-4%2Ax%2B8-5Subtract -5 from both sides to isolate y

y=-4%2Ax%2B3 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F4%29%2Ax%2B7 and goes through (2,-5) is y=-4%2Ax%2B3


So here are the graphs of the equations y=%281%2F4%29%2Ax%2B7 and y=-4%2Ax%2B3




graph of the given equation y=%281%2F4%29%2Ax%2B7 (red) and graph of the line y=-4%2Ax%2B3(green) that is perpendicular to the given graph and goes through (2,-5)