Question

Graphs help please!!!!!

Answer 1

see explanation

Explanation:

(a)

Calculate the slope m of AB using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = A(- 5, 2) and (x₂ ) = B(7, - 2)

m =
`(-2-2)/(7+5)` =
`(-4)/(12)` = -
`(1)/(3)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(3) )` = 3

Thus the slope of a line perpendicular to AB is 3

(b)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3, thus

y = 3x + c ← is the partial equation

To find c substitute C(- 2, 5) into the partial equation

5 = - 6 + c ⇒ c = 5 + 6 = 11

y = 3x + 11 ← equation of perpendicular line