Based on the equation \( y = 200 + 30x \), let's determine the responses for each part:
a) The y-intercept represents the base price of $ 200 for airfare from NYC.
b) The slope represents a cost of 30 cents per mile traveled.
c) According to the equation given, someone who traveled 2,000 miles from NYC would pay $ 800 for their airfare. (Calculation: \( y = 200 + 30(2000) = 200 + 60000 = 60200 \))
d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles. (Calculation: Set \( y = 500 \): \( 500 = 200 + 30x \) → \( 300 = 30x \) → \( x = 10 \))
e) If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 30x.
Now you can fill the responses as follows:
a) 200
b) 30
c) 800
d) 1000
e) y = 50 + 30x