Question

The graph relates the distance traveled by Train A, in miles, and the time taken, in hours. The table shows the distance traveled by Train B, in miles, and the time taken, in hours.

Answer 1

Answer:A)

Yes, the relationship is proportional.

B)

66,000 miles.

Step-by-step explanation:

A)

Yes, the graph represents a proportional relationship.

Since, A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y=kx

for some constant k , called the constant of proportionality .

As y=12000x hence the relationship is proportional.

B)

We calculate the equation of the graph with the help of two points on the graph namely (2,24000) and (4,48000) with the help of slope-intercept form of the line.

y=mx+c where m denotes the slope of the line and c denotes the y-intercept of the line.

Here when x=2 y=24000 and when x=4 y=48000

Hence, 24000=2x+c

and 48000=4x+c

on subtracting the above two equations we have:

m=12000 and c=0

Hence, the equation of line is y=12000x

Now the value at x=5.5 is:

y=12000×5.5=66,000

Hence, the number of miles the probe travels in 5.5. hours is 66,000 miles.

Step-by-step explanation: