Question

The graph below shows the distances, in miles, that a dragonfly can travel in a certain number of hours

A graph titled Motion of a Dragonfly shows Time in hours on the x axis and Distance in miles on the y axis. The scale on the x axis shows number from 0 to 10 at increments of 2, and on the y axis, the numbers are shown from 0 to 350 at increments of 70. A straight line joins the ordered pairs 0, 0 and 2, 70 and 4, 140 and 6, 210

Based on the graph, what is the dependent variable, what is the equation relating the two variables, and how far will the dragonfly travel in 24 hours if it continues to fly at the same speed?

The dependent variable is distance, the equation is x = 35y, and the dragonfly will travel 920 miles.
The dependent variable is distance, the equation is y = 35x, and the dragonfly will travel 840 miles.
The dependent variable is time, the equation is x = 35y, and the dragonfly will travel 920 miles.
The dependent variable is time, the equation is y = 35x, and the dragonfly will travel 840 miles.

Answer 1

Answer: Your answer would be x = 35y, and the dragonfly will travel 920 miles.

Explanation:

I honestly don't really have a good explanation for this because it is my first time, so if this answer is wrong, please let me, I would love to learn from my mistake!

Thanks!

Answer 2

The dependent variable is distance, the equation is y = 35x, and the dragonfly will travel 840 miles.

Explanation:

By the graph it can be seen that the distance a dragonfly can travel is dependent on the certain number of hours.

∴ Dependent variable : Distance (on y axis)

The equation of straight line is given by :-

`y=mx+c`, here m is the slope of the line and c is the initial value of y at x=0.

From the given graph, the slope of the given line passing from (0,0) and (2,70) will be :-

`m=(70-0)/(2-0)=35`

Also, the value of y = 0 at x=0.

∴ The equation of the given line :
`y=35x`

At x=24,
`y=35(24)=840`

∴ The dragonfly will travel 840 miles in 24 hours.