SOLUTION: I need help. This question says, A line goes through the point (-8,-2) and is also perpendicular to the line y= 4x - 6. Find the equation of the line. How do you do this ??

Algebra ->  Linear-equations -> SOLUTION: I need help. This question says, A line goes through the point (-8,-2) and is also perpendicular to the line y= 4x - 6. Find the equation of the line. How do you do this ??       Log On


   

Question 763078: I need help. This question says, A line goes through the point (-8,-2) and is also perpendicular to the line y= 4x - 6. Find the equation of the line. How do you do this ??
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 4, 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%284%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F4%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%2F4 Multiply the fractions.


So the perpendicular slope is -1%2F4



So now we know the slope of the unknown line is -1%2F4 (its the negative reciprocal of 4 from the line y=4%2Ax-6). Also since the unknown line goes through (-8,-2), 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%2B2=%28-1%2F4%29%2A%28x%2B8%29 Plug in m=-1%2F4, x%5B1%5D=-8, and y%5B1%5D=-2



y%2B2=%28-1%2F4%29%2Ax%2B%281%2F4%29%28-8%29 Distribute -1%2F4



y%2B2=%28-1%2F4%29%2Ax-8%2F4 Multiply



y=%28-1%2F4%29%2Ax-8%2F4-2Subtract -2 from both sides to isolate y

y=%28-1%2F4%29%2Ax-8%2F4-8%2F4 Make into equivalent fractions with equal denominators



y=%28-1%2F4%29%2Ax-16%2F4 Combine the fractions



y=%28-1%2F4%29%2Ax-4 Reduce any fractions

So the equation of the line that is perpendicular to y=4%2Ax-6 and goes through (-8,-2) is y=%28-1%2F4%29%2Ax-4


So here are the graphs of the equations y=4%2Ax-6 and y=%28-1%2F4%29%2Ax-4




graph of the given equation y=4%2Ax-6 (red) and graph of the line y=%28-1%2F4%29%2Ax-4(green) that is perpendicular to the given graph and goes through (-8,-2)