How do you write the point-slope form of the equation that has a slope of -5/6 point (8,-4)

Step-by-step explanation:

the equation of a line in

point-slope form

is.

xy − y1 = m(x−x1)

where m is the slope and (x1 - y1 ) a point on the line

to calculate m use the

gradient formula

m= y2−y1

     x2−x1

let ( x1 , y1) =( 8, 5) and ( x2 ,y2 ) = (0, −4)

⇒ m= -4-5/0-8= -9/-8= 9/8

using m= 9/8 and (x1- y1) = (8,5) then

y-5= 9/8(x-8)

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours