Question

Find the slope of the line passing through the points (4,4) and (6, -5)

Answer 1

I not sure if you mean the gradient of the line or the equation, so here is both.

Gradient (=m) :

( 4, 4 ) ( 6, 5 )
( x1 , y1) ( x2, y2 )

m = y2-y1 / x2-x1
= -5-4 / 6 - 4

= -9 / 2 (as a fraction)
= -4.5 (as a decimal)

Equation of the line :

m = -9/2

( 4, 4 )
( a, b )

y - b =m (x - a)
y - 4= -9/2 (x - 4)
(Multiply both sides by 2 to get rid of fraction)
2y - 4 = -9 (x - 4)
2y - 4 = -9x + 36
2y = -9x + 36 + 4
2y = -9x + 40

2y + 9x = 40

Please feel free to ask if you have any questions

Answer 2

M= -9/2
(6,-5) and (4,4)
4 is y1 & -5 is y2
4 is x1 &6 is x2
-5 - 4 = -9
6 - 4 = 2
-9/2 is your answer but if you simplify it then you will get 4.5