a) The y-intercept represents the base price of $ _
for airfare from NYC.
b) The slope represents a cost of _ cents per mile traveled.
c) According to the equation given, someone who traveled 2,000 miles from NYC would pay $_
for their airfare.
d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled
_ miles.
e) If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be _
Word bank:
y = 50 + 0.30x
30
200
y = 30 + 0.50x
800
1000
a) The y-intercept represents the base price of $30 for airfare from NYC.
Explanation: The y-intercept is the point where the line crosses the y-axis. In the equation of a straight line y = mx + b, 'b' represents the y-intercept, which is the value of y when x (the independent variable) is zero. In this context, it means the base price of the airfare because it's the cost of the ticket when zero miles are traveled.
b) The slope represents a cost of 30 cents per mile traveled.
Explanation: In the equation of a straight line y = mx + b, 'm' represents the slope, which indicates how much y changes for a one-unit change in x. In this case, the slope of 0.30 means that for every mile traveled, the cost increases by $0.30, or 30 cents.
c) According to the equation given, someone who traveled 2,000 miles from NYC would pay $630 for their airfare.
Explanation: Using the equation y = 30 + 0.30x, where x is the number of miles traveled, you would calculate the total cost for 2,000 miles as follows: y = 30 + 0.30(2000) = 30 + 600 = $630.
d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1,566.67 miles. However, since airfare is typically not sold in fractions of a mile, it would make more sense to either round this number or to assume we cannot determine the exact miles traveled from this information alone without more context.
Explanation: We can rearrange the equation to solve for x when y (total cost) is $500:
500 = 30 + 0.30x
500 - 30 = 0.30x
470 = 0.30x
470/0.30 = x
x = 1,566.67
e) If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x
Explanation: If the base cost changes, but the cost per mile (slope) remains the same, we simply replace the y-intercept value (initial base cost) in the original equation with the new base cost. In this case, the base cost changes from $30 to $50, while the slope (0.30 representing 30 cents per mile) stays the same.
Not you’re wrong, you can only use the words in the word bank once
My apologies for the oversight. Let's correct the responses using the word bank and use each word only once.
a) The y-intercept represents the base price of $30 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 $630 for their airfare.
To solve for "someone who traveled 2,000 miles", we would apply the given equation y = 30 + 0.30x by substituting x with 2,000:
y = 30 + 0.30(2,000)
y = 30 + 600
y = $630
d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1,566.67 miles approximately. To match with the word bank, the closest option is 1,500 miles or 1,600 miles, none of which is entirely accurate. If we round the value to the nearest hundred, the answer would be 1,600 miles.
To solve for "someone who paid $500", we would rearrange the equation:
500 = 30 + 0.30x
500 - 30 = 0.30x
470 = 0.30x
x = 470 / 0.30
x = 1,566.67 miles
We would typically round this value if we are using a word bank that restricts us to explicit numbers, so rounding to the nearest hundred gives us 1,600 miles.
e) If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x
This retains the original slope (cost per mile) but updates the y-intercept to reflect the new base cost of $50.
Please note that without rounding and given the restrictions from the word bank, the answers for parts c) and d) are best approximations with the provided options.
You’re answers b, c , d are wrong
Let's try again, adhering to the use of the words provided in the word bank and using each only once.
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.
Using the equation y = 200 + 0.30x, where x is the number of miles traveled, you would calculate the total cost for 2,000 miles as follows: y = 200 + 0.30(2000) = 200 + 600 = $800.
d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1,000 miles.
Starting with the equation y = 200 + 0.30x and knowing that y is $500:
500 = 200 + 0.30x
300 = 0.30x
300/0.30 = x
1000 = x
e) If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x
This reflects the updated y-intercept (base cost) of $50 while retaining the slope of 0.30 (cost per mile).
a) To find the base price of airfare from NYC, you can look at the given equation y = 30 + 0.30x. The y-intercept represents the value of y (the cost of airfare) when x (the distance traveled) is zero. In this case, the y-intercept is 30. Therefore, the base price for airfare from NYC is $30.
b) The slope of the equation y = 30 + 0.30x represents the rate of change in y (the cost of airfare) with respect to x (the distance traveled). In this case, the slope is 0.30. To interpret this, we can say that for every one unit increase in x (distance traveled), the cost of airfare increases by 0.30 units of currency. Since the units of x are miles, we can conclude that the cost of airfare increases by 30 cents for each mile traveled.
c) To calculate the cost of airfare for someone who traveled 2,000 miles from NYC, we can substitute x = 2000 into the equation y = 30 + 0.30x. Plugging in the value, we get y = 30 + 0.30 * 2000 = 30 + 600 = $630. Therefore, someone who traveled 2,000 miles from NYC would pay $630 for their airfare.
d) To find the number of miles traveled by someone who paid $500 for airfare from NYC, we can rearrange the equation y = 30 + 0.30x to solve for x. In this case, the value of y is $500. So, we have 500 = 30 + 0.30x. By rearranging the equation and solving for x, we get 470 = 0.30x. Dividing both sides by 0.30, we find x = 470 / 0.30 = 1566.67. Therefore, someone who paid $500 for airfare from NYC would have traveled approximately 1567 miles.
e) If the base cost for airfare changes to $50 (represented by a new y-intercept), and assuming the cost per mile remains unchanged at 0.30 (represented by the slope), the new equation representing the airfare is y = 50 + 0.30x. This means the cost starts at $50 and increases by 30 cents for each mile traveled.