Write an equation of the line containing the given point and perpendicular to the given line. Express your answer in the form y=mx+b. (5.6), 8x +y =4
The equation of the line is y=
(Simplify your answer. Use integers or fractions for any numbers in the expression)

Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of -6, 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%28-6%2F1%29 So plug in the given slope to find the perpendicular slope

m%5Bp%5D=%28-1%2F1%29%281%2F-6%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%2F6 Multiply the fractions.

So the perpendicular slope is 1%2F6

So now we know the slope of the unknown line is 1%2F6 (its the negative reciprocal of -6 from the line y=-6%2Ax%2B8). Also since the unknown line goes through (3,6), 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-6=%281%2F6%29%2A%28x-3%29 Plug in m=1%2F6, x%5B1%5D=3, and y%5B1%5D=6

y-6=%281%2F6%29%2Ax-%281%2F6%29%283%29 Distribute 1%2F6

y-6=%281%2F6%29%2Ax-3%2F6 Multiply

y=%281%2F6%29%2Ax-3%2F6%2B6Add 6 to both sides to isolate y

y=%281%2F6%29%2Ax-3%2F6%2B36%2F6 Make into equivalent fractions with equal denominators

y=%281%2F6%29%2Ax%2B33%2F6 Combine the fractions

y=%281%2F6%29%2Ax%2B11%2F2 Reduce any fractions

So the equation of the line that is perpendicular to y=-6%2Ax%2B8 and goes through (3,6) is y=%281%2F6%29%2Ax%2B11%2F2

So here are the graphs of the equations y=-6%2Ax%2B8 and y=%281%2F6%29%2Ax%2B11%2F2

graph of the given equation y=-6%2Ax%2B8 (red) and graph of the line y=%281%2F6%29%2Ax%2B11%2F2(green) that is perpendicular to the given graph and goes through (3,6)

(3,6)

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