Part A
x = time in seconds that have gone by
y = distance in meters Superman is away from Lois
"After flying for 15 seconds, he is 2100 meters from her" means we have the point (x,y) = (15, 2100)
"at 18 seconds he is 1980 meters from her" tells us we have a second point (x,y) = (18,1980)
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Find the slope of the line through these two points
m = (y2-y1)/(x2-x1)
m = (1980-2100)/(18-15)
m = (-120)/(3)
m = -40
The slope is -40 which means Superman is getting 40 meters closer each second. I.e, the distance is dropping 40 meters per second
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Use one of the points and the slope to find the y intercept b
y = mx+b
2100 = (-40)*15 + b
2100 = -600 + b
2100+600 = b
b = 2700
This is the starting distance Superman is away from Lois
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Since m = -40 and b = 2700, we know the y = mx+b equation becomes y = -40x+2700.
Replace x with s, replace y with m. We now have m = -40s+2700
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<h3>Final Answer: m = -40s+2700</h3>
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Part B
Plug s = 6 into the equation we found for part A. Then simplify.
m = -40s+2700
m = -40*6+2700
m = -240+2700
m = 2460
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<h3>Final Answer: 2460 meters</h3>
