SOLUTION: The slope of a line is –4 and its y-intercept is (0, 4). What is the equation of the line that is perpendicular to the first line and passes through (–8, 2)?

Algebra ->  Linear-equations -> SOLUTION: The slope of a line is –4 and its y-intercept is (0, 4). What is the equation of the line that is perpendicular to the first line and passes through (–8, 2)?      Log On


   

Question 733698: The slope of a line is –4 and its y-intercept is (0, 4). What is the equation of the line that is perpendicular to the first line and passes through (–8, 2)?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The slope of a line is m=-4 and its y-intercept is (0, 4).
so, the equation of this line is:
y=mx%2Bb....plug in given values m=-4and y=4
y=-4x%2B4.......the first line


the equation of the line that is perpendicular to the first line and passes through (-8, 2) will be:
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%28-4%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-4%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%2B4). 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-2=%281%2F4%29%2A%28x%2B8%29 Plug in m=1%2F4, x%5B1%5D=-8, and y%5B1%5D=2



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



y-2=%281%2F4%29%2Ax%2B8%2F4 Multiply



y=%281%2F4%29%2Ax%2B8%2F4%2B2Add 2 to both sides to isolate y

y=%281%2F4%29%2Ax%2B8%2F4%2B8%2F4 Make into equivalent fractions with equal denominators



y=%281%2F4%29%2Ax%2B16%2F4 Combine the fractions



y=%281%2F4%29%2Ax%2B4 Reduce any fractions

So the equation of the line that is perpendicular to y=-4%2Ax%2B4 and goes through (-8,2) is y=%281%2F4%29%2Ax%2B4


So here are the graphs of the equations y=-4%2Ax%2B4 and y=%281%2F4%29%2Ax%2B4




graph of the given equation y=-4%2Ax%2B4 (red) and graph of the line y=%281%2F4%29%2Ax%2B4(green) that is perpendicular to the given graph and goes through (-8,2)