Let's break down the questions based on the information provided:
a) The y-intercept represents the base price of airfare from NYC.
- The base price (y-intercept) given in the options is 30.
b) The slope represents a cost of ______ cents per mile traveled.
- The slope given in the options is 0.30, which means 30 cents per mile.
c) According to the equation given, someone who traveled 2,000 miles from NYC would pay $ ______ for their airfare.
- If the slope is 0.30 (30 cents per mile), then for 2,000 miles: \[ \text{Cost} = \text{Base Price} + (\text{Slope} \times \text{Distance}) \] Therefore: \[ \text{Cost} = 30 + (0.30 \times 2000) = 30 + 600 = 630 \]
- So, the answer for this is 630.
d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled _____ miles.
- Using the equation: \[ 500 = 30 + 0.30x \] Rearranging gives: \[ 500 - 30 = 0.30x \implies 470 = 0.30x \implies x = \frac{470}{0.30} = 1566.67 \text{ (approx)} \]
- Since we need a whole number, we can find this to be approximately 1566 miles.
e) If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be _____.
- The new equation with a base price of 50 and the same cost per mile (0.30) would be: \[ y = 50 + 0.30x \]
- According to the options, that is not listed, so responding is not possible.
Bringing this all together, the final responses will be:
a) 30
b) 30
c) 630
d) 1567 (or next closest if round numbers were not provided, potentially 2000 as distance)
e) y = 50 + 0.30x