Use the image to answer the question.
A line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 14 right parenthesis; left parenthesis 4 comma 28 right parenthesis; left parenthesis 6 comma 42 right parenthesis; left parenthesis 8 comma 56 right parenthesis; left parenthesis 10 comma 70 right parenthesis; and left parenthesis 12 comma 84 right parenthesis.
Using the points shown in the graph, identify the constant of proportionality for this graph.
(1 point)
$$
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To find the constant of proportionality for this graph, we can use the formula:
constant of proportionality = difference in y-coordinates / difference in x-coordinates
Let's choose two points on the line: (0, 0) and (2, 14).
The difference in y-coordinates is 14 - 0 = 14.
The difference in x-coordinates is 2 - 0 = 2.
So the constant of proportionality is 14 / 2 = 7.
Therefore, the constant of proportionality for this graph is 7.
Use the image to answer the question.
A graph with an x-axis representing time in minutes ranges from 0 to 4.5 in increments of 0.5. The y-axis representing distance in feet ranges from 0 to 9 in unit increments. A line is labeled speed of a sloth. The line passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 0.5 comma 3 right parenthesis; left parenthesis 1 comma 6 right parenthesis; and left parenthesis 1.5 comma 9 right parenthesis.
Identify the distance a sloth travels per minute.
(1 point)
ft. per minute
To find the distance a sloth travels per minute, we need to find the slope of the line.
Let's choose two points on the line: (0, 0) and (1, 6).
The difference in y-coordinates is 6 - 0 = 6.
The difference in x-coordinates is 1 - 0 = 1.
So the slope of the line, and therefore the distance the sloth travels per minute, is 6/1 = 6 ft.
Therefore, the sloth travels 6 feet per minute.
To find the constant of proportionality, we need to examine the relationship between the x-values and the y-values.
First, we can see that the x-values increase by 2 each time: 0, 2, 4, 6, 8, 10, 12.
Next, let's look at the corresponding y-values:
For x = 0, y = 0.
For x = 2, y = 14.
For x = 4, y = 28.
For x = 6, y = 42.
For x = 8, y = 56.
For x = 10, y = 70.
For x = 12, y = 84.
To find the constant of proportionality, we can divide each y-value by its corresponding x-value:
For x = 2, y/x = 14/2 = 7.
For x = 4, y/x = 28/4 = 7.
For x = 6, y/x = 42/6 = 7.
For x = 8, y/x = 56/8 = 7.
For x = 10, y/x = 70/10 = 7.
For x = 12, y/x = 84/12 = 7.
As we can see, the value of y/x is always 7. Therefore, the constant of proportionality for this graph is 7.