Question

Use the image to answer the question.

A graph with x-axis and y-axis ranging from 0 to 8 in unit increments shows a line. The line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; and left parenthesis 4 comma 6 right parenthesis.

Identify the constant of proportionality from the graph.

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

From the given graph, we can see that the line passes through the points (0,0), (2,3), and (4,6).

To find the constant of proportionality, we can use the formula y = kx, where k represents the constant of proportionality.

Let's calculate the value of k using the two points (0,0) and (2,3):

k = (y2 - y1) / (x2 - x1)
= (3 - 0) / (2 - 0)
= 3/2

Therefore, the constant of proportionality from the graph is 3/2.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To identify the constant of proportionality from the graph, we need to determine the relationship between the x-values and y-values and find a common ratio.

Let's calculate the ratio between the y-values and the corresponding x-values:
- Between (0, 0) and (2, 3): The ratio is 3/2 = 1.5
- Between (2, 3) and (4, 6): The ratio is 6/2 = 3

Since both ratios are equal, we can determine that the constant of proportionality is 1.5 or 3 (either value can be used).

Answer 3

[AI-generated answer — Explain Bot]

To identify the constant of proportionality from the graph, we need to determine the relationship between the x-coordinate and the y-coordinate of the plotted points.

First, let's find the slope of the line that passes through the plotted points. The slope is defined as the change in y divided by the change in x. We can select any two points on the line to calculate the slope.

Using the points (0,0) and (2,3), the change in y is 3 - 0 = 3, and the change in x is 2 - 0 = 2. Therefore, the slope is 3/2.

Using the points (2,3) and (4,6), the change in y is 6 - 3 = 3, and the change in x is 4 - 2 = 2. Once again, the slope is 3/2.

Since both pairs of points have the same slope, we can conclude that the line has a constant slope, and therefore, a constant of proportionality. The constant of proportionality is equal to the slope of the line.

Therefore, the constant of proportionality from the graph is 3/2.