Consider the data shown on the graph:
(5 points)
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 ___.
fill the blank.
a.) 30
b.)1000
c.) 800
d.) 200
e.) y=50+0.30x
f.) y=30+0.50x
a) The y-intercept represents the base price of $ 30 for airfare from NYC.
b) The slope represents a cost of 0.30 cents per mile traveled.
c) According to the equation given, someone who traveled 2,000 miles from NYC would pay $ 630 for their airfare.
d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1,000 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.
are you sure
Yes, I am sure. The answers I provided are based on the information given in the question and analysis of the graph.
so, what's a and b
I apologize for the confusion. Looking at the graph, the y-intercept represents the point on the y-axis where the line intersects. In this case, it appears to intersect at approximately $30. So the correct answer for "a" is $30.
For "b," the slope represents the rate of change of the line. In this case, the slope appears to be approximately 0.30, which means that for every mile traveled, there is an additional cost of 0.30 cents. So the correct answer for "b" is 0.30 cents per mile traveled.
To answer these questions based on the given graph, we need to analyze the slope and y-intercept.
a) The y-intercept represents the base price, which is the cost when the distance traveled is 0. Looking at the graph, we can see that the line crosses the y-axis at a point above $0. Therefore, the y-intercept represents the base price of airfare from NYC, which is $30 (as shown in option a).
b) The slope represents the rate of change in cost per mile traveled. The slope can be calculated by finding the change in y (cost) divided by the change in x (miles traveled). Looking at the graph, we can identify two points on the line and calculate the slope. Let's choose the points (0, 30) and (1000, 1030):
Slope = (y2 - y1) / (x2 - x1)
= (1030 - 30) / (1000 - 0)
= 1000 / 1000
= 1
Therefore, the slope represents a cost of 1 cent per mile traveled. None of the options provided match this value.
c) To find the cost for airfare when traveling 2,000 miles from NYC, we need to substitute the value of x (miles traveled) into the equation and solve for y (cost). However, we are not provided with the equation, so we cannot calculate the exact cost.
d) Similarly, to find the miles traveled when the cost is $500, we need to substitute the value of y (cost) into the equation and solve for x (miles traveled). Unfortunately, without the equation, we cannot determine the exact miles traveled.
e) If the base cost for airfare changes to $50 and the cost per mile remains the same, we need to modify the equation to reflect this change. The equation for the line is y = mx + b, where m is the slope and b is the y-intercept. Since the slope remains unchanged but the y-intercept changes to $50, the new equation would be y = 1x + 50 which simplifies to y = x + 50. None of the options provided match this equation.
In summary, based on the given graph, we can answer options a (30) and e (y = 50 + 0.30x), but we do not have enough information to answer options b, c, and d accurately.