Let's analyze the equation \( y = 200 + 0.30x \).
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The y-intercept represents the base price of $________ for airfare from NYC?
- The y-intercept is the value of \( y \) when \( x = 0 \). From the equation, when \( x = 0 \): \[ y = 200 + 0.30(0) = 200 \]
- Therefore, the base price of airfare from NYC is $200.
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The slope represents a cost of _______ cents per mile traveled?
- The slope \( 0.30 \) in the equation indicates the cost per mile. Since the slope is in dollars, we convert it to cents (1 dollar = 100 cents): \[ 0.30 \text{ dollars} = 0.30 \times 100 = 30 \text{ cents} \]
- So, the slope represents a cost of 30 cents per mile traveled.
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According to the equation given, someone who traveled 2,000 miles from NYC would pay _______ for their airfare?
- We can find out how much someone would pay for traveling 2,000 miles by substituting \( x = 2000 \) into the equation: \[ y = 200 + 0.30(2000) = 200 + 600 = 800 \]
- Therefore, someone who traveled 2,000 miles from NYC would pay $800 for their airfare.
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According to the given equation, someone who paid $500 for airfare from NYC would have traveled ________ miles?
- We set \( y = 500 \) and solve for \( x \): \[ 500 = 200 + 0.30x \] \[ 500 - 200 = 0.30x \] \[ 300 = 0.30x \] \[ x = \frac{300}{0.30} = 1000 \]
- Therefore, someone who paid $500 for airfare from NYC would have traveled 1,000 miles.
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If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be________?
- If the base cost changes to $50, we keep the slope the same (0.30). Thus, the new equation becomes: \[ y = 50 + 0.30x \]
- Therefore, the new equation would be \( y = 50 + 0.30x \).
5 answers