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)
answer:(3,6)
