Help me What is the constant of proportionally, K?

Determine the distance in miles traveled bye the probe in 5.5 hours

I) Yes, the graph represent a proportional relationship

ii) 1200miles/hour

iii) 66,000miles/hour

Question:

The complete question related to this found at (question:14811794) is stated below:

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.

What is the constant of proportionally, k?

Determine the number of miles the probe travels in 5.5 hours.

Step-by-step explanation:

Find attached the graph.

i) We are informed the graph shows the relationship between x.

For the graph to represent a proportional relationship, it must meet the condition y = kx

Where y is the dependent variable

x is the independent variable

k = constant of proportionality

From the graph, y = distance in miles

x= time in hours

y = kx is a linear equation with no intercept

The graph shows a straight line starting from origin. Therefore, the graph represent a proportional relationship.

ii) To determine k, we pick any value of y that corresponds to a value of x on the graph and insert in the equation: y = kx

For coordinates (2, 24000)

When y = 24000miles, x = 2hours

24000 = k × 2

k = 24000/2 = 12000miles/hour

Therefore, the constant of proportionally, k = 12000miles/hour

ii) To determine the number of miles the probe travels in 5.5 hours, we would use the relationship between y and x.

since k = 12000, the relationship:

y = 12000x

When x = 5.5hours, y = ?

y = 12000×5.5

y = 66,000miles/hour

Therefore, the number of miles the probe travels in 5.5 hours = 66,000miles/hour

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