A boat is traveling through the water. The graph below shows the relationship between the distance D (in kilometers) and the time T (in hours) the boat has traveled.
Distance (kilometers)
D50100150200250300350400450500T1234567890
Time (hours)
(a)Write an equation to represent the relationship between D and T.
(b)Choose the correct statement to represent this relationship.
The boat is traveling 1 kilometer per 50 hours.
The boat is traveling 50 kilometers per hour.
The boat is traveling 100 kilometers per hour.
The boat is traveling 1 kilometer per 100 hours.
(a) Let's look at the graph to find the relationship between D and T. We see that for every increase of 1 hour in T, there is a corresponding increase of 50 kilometers in D.
So, we can write the equation for this relationship as:
D = 50T
(b) The correct statement to represent this relationship is:
The boat is traveling 50 kilometers per hour.
(a) To write an equation for the relationship between distance D and time T, we need to examine the graph points. From the graph, we can observe that the distance increases linearly with time.
We can see that for every 1 hour of travel, the boat covers 50 kilometers. Therefore, the equation representing the relationship between D and T is:
D = 50T
(b) The correct statement to represent this relationship is:
The boat is traveling 50 kilometers per hour.
To determine the relationship between the distance D (in kilometers) and the time T (in hours), we can analyze the graph given.
(a) Equation to represent the relationship between D and T:
Looking at the graph, we can see that the distance increases linearly with time. Therefore, we can use the equation of a straight line, which is in the form y = mx + b.
In this case, D represents the y-axis (dependent variable) and T represents the x-axis (independent variable). The slope m of the line represents the rate of change, which is the speed of the boat.
To find the equation, we need to determine the slope and y-intercept from the graph.
Slope (m) = rise / run
From the graph, we can see that for every increase of 1 hour (run), the distance increases by 50 kilometers (rise). Therefore, the slope (m) is 50.
Now, let's determine the y-intercept (b) by looking at where the line intersects the y-axis. From the graph, we can see that when T = 0, D = 0. This means the boat started at the origin. Therefore, the y-intercept (b) is 0.
Now we can plug in the values into the equation:
D = 50T + 0
Simplifying the equation:
D = 50T
Therefore, the equation representing the relationship between D and T is D = 50T.
(b) Statement to represent this relationship:
From the equation D = 50T, we can interpret it as "The boat is traveling 50 kilometers per hour."
Therefore, the correct statement is "The boat is traveling 50 kilometers per hour."