Question

The graph shows the relationship between x, the amount of time in hours and y, the distance traveled in miles, by a probe before it reaches Mars. Does the graph represent a proportional relationship? Justify your answer. Determine the number of miles the probe travels in 5.5 hours.

Answer 1

Answer: 1) Yes because it’s a straight line and it goes though the origin (0,0). 2) 66,000 miles

Step-by-step explanation:

1) Two variables y and x are said to be in a proportional relationship with each other when there exist a relationship in the form: where (k) is called "constant of proportionality" In other words, two variables are in a proportional relationship if, when one of the two variable increases, the other one increases by the same proportion.In this problem, the two variables represented are distance (y-axis) and time (x-axis); from the graph, we see that their relationship is represented by a straight line, which is in the form ; therefore, the two variables are in a proportional relationship.

2) We can find the constant of proportionality by re-arranging the equation: And by taking the values of y and x at a certain point along the graph.For instance, by takingx = 4 h d = 48,000 miles. We find which means that the probe travels 12,000 miles per hour. Therefore, we can now find the distance travelled by the probe when x = 5.5

Answer 2

1) Yes

2) 66,000 miles

Explanation:

1)

The graph is missing, so you can find it in attachment.

Two variables y,x are said to be in a proportional relationship with each other when there exist a relationship in the form:

`y=kx`

where

k is called "constant of proportionality"

In other words, two variables are in a proportional relationship if, when one of the two variable increases, the other one increases by the same proportion.

In this problem, the two variables represented are distance (y-axis) and time (x-axis); from the graph, we see that their relationship is represented by a straight line, which is in the form
`y=kx`; therefore, the two variables are in a proportional relationship.

2)

We can find the constant of proportionality by re-arranging the equation:

`k=(y)/(x)`

And by taking the values of y and x at a certain point along the graph.

For instance, by taking

x = 4 h

d = 48,000 mi

We find

`k=(48,000)/(4)=12,000 mi/h`

which means that the probe travels 12,000 miles per hour.

Therefore, we can now find the distance travelled by the probe when

x = 5.5 h

We find:

`y=kx=(12,000)(5.5)=66,000 mi`