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

1) Yes

2) 66,000 miles

Step-by-step 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:

$k=\frac{y}{x}$

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

$k=\frac{48,000}{4}=12,000 mi/h$

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:

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