What is the slope of the line perpendicular to # y=1/8x+ 7 #?
If 2 lines are perpendicular to each other then the product of their gradients is equal to -1 .
If gradients of 2 perpendicular lines are
# m_1 color(black)(" and ") m_2#
# m_1 xx m_2 = -1 #
# y = 1/8 x + 7 #
is of the form y = mx + c , where m represents the gradient and c , the y-intercept.
hence this line has
# m = 1/8 #
m of perpendicular is found using the above relationship.
# 1/8 xx m_2 = -1 rArr m_2 = -1/(1/8) = -8 #
The product (result of multiplication) of slopes of perpendicular lines is -1.
Because the product of perpendicular lines' slopes is -1, we can work out the slope of the perpendicular line. Since we do not have to worry about the constant at the end, we can attempt to write down an equation.
This resulting equation gives us the slope of the perpendicular line in which X is the value of the slope that we are looking for -- (1/8) * X = -1.
Easily, we can approach this by dividing -1 by 1/8. This gives us -1/1/8. A fraction that looks this hideous is definitely not the answer, so what do we do?
We divide and simplify this monster by using a couple of rules.
First, we flip 1/8 into 8/1. And we suddenly find that 8/1 is 8, for the fact that anything over 1 is itself.
Then, we put this number (8) on top and the number originally there (-1) o the bottom. This kind of division requires that the bottom fraction gets flipped and switched with the top number.
Finally, we come to the concluding equation that X=8/-1. 8 divided by negative 1 is....well, -8! Hence, the answer is -8. If you don't believe it, go get a graphing device and enter the equation above, and enter another equation in the form of -8X+/-C.
Randomly decide what C is and you'll find that whatever you do, the line you created is perpendicular to the line (1/8)X+7.