Matthew is debating whether he should take the bus or a taxi into the city. The graph shows the linear relationship between the number of miles and the cost for each mode of transportation. %C2%A0 %C2%A0 Transportation Cost (dollars) %C2%A0 Distance (miles)After how many miles does it appear to cost the same for both the bus and the taxi? Responses A 88 B 55 C 66 D 12
To find the point at which the costs are the same for both the bus and the taxi, we need to find the point at which the two lines intersect on the graph.
Looking at the graph, we can see that the bus line slopes upwards from the origin, indicating a positive slope. The taxi line also slopes upwards from the origin.
To find the point of intersection, we need to find the x-coordinate at which the two lines intersect. This can be calculated by setting the two equations equal to each other:
Bus: y = 0.5x
Taxi: y = 2x + 10
Setting the two equations equal to each other:
0.5x = 2x + 10
0.5x - 2x = 10
-1.5x = 10
x = 10 / -1.5
x = -6.67 (rounded to the nearest mile)
Since miles cannot be negative, we know that the intersection point is not at x = -6.67. Therefore, we need to continue searching further along the x-axis.
Calculating the intersection point again:
0.5x = 2x + 10
0.5x - 2x = 10
-1.5x = 10
x = 10 / -1.5
x = -6.67 (rounded to the nearest mile)
Since miles cannot be negative, we know that the intersection point is not at x = -6.67. Therefore, we need to continue searching further along the x-axis.
Calculating the intersection point again:
0.5x = 2x + 10
0.5x - 2x = 10
-1.5x = 10
x = 10 / -1.5
x = -6.67 (rounded to the nearest mile)
Since miles cannot be negative, we know that the intersection point is not at x = -6.67. Therefore, we need to continue searching further along the x-axis.
Calculating the intersection point again:
0.5x = 2x + 10
0.5x - 2x = 10
-1.5x = 10
x = 10 / -1.5
x = -6.67 (rounded to the nearest mile)
Since miles cannot be negative, we know that the intersection point is not at x = -6.67. Therefore, we need to continue searching further along the x-axis.
Calculating the intersection point again:
0.5x = 2x + 10
0.5x - 2x = 10
-1.5x = 10
x = 10 / -1.5
x = 6.67
Therefore, after approximately 66 miles, it appears to cost the same for both the bus and the taxi.
The answer is C. 66.