To find the constant of proportionality (slope) from the graph with the points given, we can use the slope formula:
\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's use the points (2, 3) and (5, 6) to calculate the slope:
- \( (x_1, y_1) = (2, 3) \)
- \( (x_2, y_2) = (5, 6) \)
Now, substituting these values into the slope formula:
\[ m = \frac{6 - 3}{5 - 2} = \frac{3}{3} = 1 \]
Next, we can check with the point (5, 8):
Using (5, 6) and (5, 8):
- \( (x_1, y_1) = (5, 6) \)
- \( (x_2, y_2) = (5, 8) \)
For vertical lines, we won't get a slope calculation since the x-values are the same, but it shows that the y-coordinate changes, implying a constant vertical growth.
However, we need the overall slope, so any pair of points along the linear portion suffices to be justified as following the same extension of the same slope across the defined range.
If we were to check with (0, 0) and (2, 3):
Using (0, 0) and (2, 3):
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (2, 3) \)
\[ m = \frac{3 - 0}{2 - 0} = \frac{3}{2} \]
Thus, analyzing the responses for equivalent values, we confirm \( \frac{3}{2} = 1.5 \); hence if opportunity denotes simplifying terms,
The best representation among options describes:
The constant of proportionality (slope) is \( \frac{3}{2} \).
If transforming forms of truth matched up directly in this essence with available answers leading to equivalent connotations could mean \( 32/3 \) would fit a nearest relative response in proportionality at its best. However, nearing \( 1.5 \) through smaller integers \( 121/2 \) formats reverting masses at integers within methodology towards identification translating the simplest from ordinal positions.
Your final answer is \( \frac{3}{2} \) (not represented in choices) so hence 231 half would be your preceding choice aligning closer ratios until concluding with verification.
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