Answer:
The spy plane will re-fuel at coordinates ( 8, 7 )
Step-by-step explanation:
The spy plane leaves a secret runway at A (–16 , 28) and heads toward a missile factory at B.
We have to find Line 1
Runway (-16,28)
-16 = x2
28 = y2
Missile Factory
(48, –28)
48 = x1
-28 = y1
So we set up the equation:
a = y2 - y1 / x2 - x1 = 28 - (-28) / -16 - 48 = 56/-64 = -0.875
Now we must find the equaion: y = ax + b
we substitute a with -0.875
so the new equation will look like this: y = -0.875x + b
y2 = 28 = y
x2 = -16 = x
y = -0.875x + b
28 = -0.875(-16) + b
28 = 14 + b
28 - 14 = 14 - 14 + b
14 = b
so y = -0.875x + 14
Now lets solve for Line 2
we use the same formula:
a = y2 - y1 / x2 - x1 = 37 - (-13) / 56 - (-24) = 50/80 = 0.625
Now we must find the equaion: y = ax + b
we substitute a with 0.625
so the new equation will look like this: y = 0.625x + b
y2 = 37 = y
x2 = 56 = x
y = 0.625x + b
37 = 0.625(56) + b
37 = 35 + b
37 - 35 = 35 - 35 + b
2 = b
so y = 0.625x + 2
Now according to the text, it says "At what coordinates will the two planes meet to re-fuel the spy plane"
which means we have to find the point of intersection, which means we have to make both equation = to each other
so the problem would look like this:
-0.875x + 14 = 0.625x + 2
-0.875 + 0.875x + 14 = 0.625x + 0.875x + 2
14 = 1.5x + 2
14 - 2 = 1.5x + 2 - 2
12 = 1.5x
12/1.5 = 1.5x/1.5
8 = x
now that we know the x, we need to find the y
so y = 0.625x + 2 turns into
y = 0.625(8) + 2
y = 5 + 2
y = 7
so the answer is: The spy plane will re-fuel at coordinates ( 8, 7 )
