In a proportional relationship represented by the equation \( y = mx \), the value \( m \) represents the constant of proportionality or the slope of the line.
To derive the equation using the given points (1, 5) and (2, 10), we can first calculate the slope \( m \).
We can use the formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \( (1, 5) \) and \( (2, 10) \):
- \( x_1 = 1 \), \( y_1 = 5 \)
- \( x_2 = 2 \), \( y_2 = 10 \)
Now substituting into the slope formula:
\[ m = \frac{10 - 5}{2 - 1} = \frac{5}{1} = 5 \]
Now that we've determined the slope \( m = 5 \), we can write the equation of the line:
\[ y = mx = 5x \]
Thus, the equation of the line is:
\[ y = 5x \]