So you know the slope is 2/3. We can write the equation y=mx+b and plug in the value we know to get y=(2/3)x+b. Since the line goes through the point, (-5,6) our equation must be true when the x and y value are plugged into the equation. We get (6)=(2/3)(-5)+b. Solving for b, we get 6=(-10/3)+b then b=28/3. This means our formula is y=(2/3)x+28/3
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Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.
Step-by-step explanation: As it is stipulated, <u>x</u> relates to type-A and y to type-B.
Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:
60x + 80y ≤ 360
For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:
160x + 120y ≤ 680
To calculate how many of each type you need:
60x + 80y ≤ 360
160x + 120y ≤ 680
Isolating x from the first equation:
x = 
Substituing x into the second equation:
160(
) + 120y = 680
-3200y+1800y = 10200 - 14400
1400y = 4200
y = 3
With y, find x:
x = 
x = 
x = 2
To determine the cost:
cost = 42,000x + 51,000y
cost = 42000.2 + 51000.3
cost = 161400
To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400
ANSWER

EXPLANATION
We use the method of completing the squares.
The equation is

We rewrite the above equation to obtain;

We divide through by 3 to obtain;

We add half the coefficient of

to both sides of the equation to get,

The right hand side is now a perfect square.

We now take square root of both sides to get;

We add -2 to both sides,

We simplify to obtain,
A = 2+3a +6
a-3a = 8
-2a = 8
a = -8/2 = -4