Question

What’s the slope of a line perpendicular to a line through points,
E(5,7), F(3,1)

Answer 1

Two lines are perpendicular when,

`a_1=-a_2^(-1)`

Now solve for
`a_2` to get
`a_2=-a_1^(-1)`

First we calculate the slope
`a_1` from the given points
`E(x_1,y_1),F(x_2,y_2)\longrightarrow E(5,7),F(3,1)`.

`a_1=\frac{\Delta{y}}{\Delta{x}}=(y_2-y_1)/(x_2-x_1)=(1-7)/(3-5)=(-6)/(-2)=3`

Now use the first formula and insert the data in it to find the value of the second slope
`a_2`,

`a_2=-3^(-1)=\boxed{-(1)/(3)}`

And that's it.

Hope this helps.

r3t40

Answer 2

-1/3 is the slope perpendicular

Explanation:

When we have 2 points, we can use the formula

m = (y2-y1)/(x2-x1) to find the slope

m = (1-7)/(3-5)

=-6/-2

=3

The slope is 3

We want a slope perpendicular

Remember that is the negative reciprocal

- (1/3)

-1/3