Part A
The equation is d = 50t
This is because the slope of 50 represents how many miles per day the butterflies cover (on average). The y intercept is 0 to indicate that 0 miles have been traveled initially.
You can think of this as the equation y = 50x
If t = 1, then d = 50t = 50*1 = 50 miles have been covered
If t = 2, then d = 50t = 50*2 = 100 miles have been covered
And so on.
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Part B
You'll have these values in the bottom row (in the order presented): 50, 100, 150, 200, 250
You can plug in the values t = 1, t = 2, t = 3, t = 4 and t = 5 into d = 50t to find those answers in bold.
Or you could add on 50 each time to generate each new value. We start at 50 since t = 1 corresponds to d = 50.
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Part C
You can keep the pattern of 50,100,150, ... going until you reach 2500. Then note the t value that pairs with d = 2500
In my opinion, that's the slower method.
The quicker method is to plug d = 2500 into the equation for part A, and then solve for t.
d = 50t
2500 = 50t
50t = 2500
50t/50 = 2500/50 ....... divide both sides by 50
t = 50
It will take 50 days for the average distance traveled to be 2500 miles.
