Question

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

Answer 1

Answer:

-1/3 is the slope perpendicular

Step-by-step 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

Answer 2

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 $E(x_1,y_1),F(x_2,y_2)\longrightarrow E(5,7),F(3,1)$.

$a_1=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3$

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

$a_2=-3^{-1}=\boxed{-\dfrac{1}{3}}$

And that's it.

Hope this helps.

r3t40