Linear functions

[d0minicz]

A farmer measured the quantity of water in a storage tank 20 days after it was filled and found it contained 3000 litres. After a further 15 days it was measured again and found to have 1200 litres in it. Assume that the amount of water in the tank decreases at a constant rate.
a) find the relation between L, the number of litres of water in the tank, and t, the number of days ater the tank was filled.
b) How much water does the tank hold when it is full?
c) Sketch the graph of L against t for a suitable domain.
d) State this domain
e) How long does it take for the tank to empty?
f) At what rate does the water leave the tank?

I just need some hints to get started, ie. to solve part a). thanks alot flaming arrow

[Flaming_Arrow]

ok first we have to know which is x and which is y

x is the number of days because quantity of water change according to days meaning its the independent variable.

x=t
y=L

so then set up your two points then find the equation

[d0minicz]

I just cant set up the two points and find the equation.
Can you plz show me?

[d0minicz]

Oooops sorry guys i got it
used simultaneous equations

[Flaming_Arrow]

you can just use two points to get the gradient use then y= mx+ c to find the y intercept.

[d0minicz]

A boat leaves from O to sail to two islands. The boat arrives at a point A on happy island with coordinates (10, 22.5) (units are in Kms)
d) A third island lies on the perpendicular bisector of line segment AB. its port is denoted by C. It is known that the x-coordinate of C is 52. Find the y-coordinate of C.
I've found that OA => y= 9/4x
and AB => y= -27/26x + 855/26

How would i go about finding the y-coordinate of C? thanks

[Flaming_Arrow]

find the equation of the perpendicular bisector of AB(mid point of AB and perpendicular to AB) then sub in x= 52 to get the y coordinate

[Flaming_Arrow]

Another way

Mid Point of AB 

Gradient of the AB bisector

Point C 



y =

[d0minicz]

Sorry, why do you use the midpoint of AB, thanks

[Flaming_Arrow]

perpendicular bisector means a line which is perpendicular to AB through the midpoint of AB

[d0minicz]

ABCD is a parallelogram with coordinates A(2,2), B(1.5,4) and C(6,6)
c) Find the equation of the diagonals AC and BD
d) Find the coordinates of the point of intersection of the diagonals.

need hints thxx =]

[Flaming_Arrow]

c) find the gradient of AC then sub in A or C to find the equation, to find BD make equation AD and CD equal each other to get the point D then find the equation of BD
d) make the diagonals equal eachother