Create a rule for the line that contains the points (1, 1/4) and (3, 3/4)

To find the equation of the line passing through the points (1, 1/4) and (3, 3/4), we can use the point-slope form of the equation of a line:

Point-slope form: y - y_1 = m(x - x_1)

First, let's find the slope m using the given points:

m = \dfrac{y_2 - y_1}{x_2 - x_1}
m = \dfrac{\frac{3}{4} - \frac{1}{4}}{3 - 1}
m = \dfrac{\frac{2}{4}}{2} = \frac{1}{4}

Now, choose one of the points to substitute into the point-slope form. Let's use the point (1, 1/4):

y - \frac{1}{4} = \frac{1}{4}(x - 1)
y - \frac{1}{4} = \frac{1}{4}x - \frac{1}{4}

Now, simplify the equation:

y = \frac{1}{4}x

Therefore, the rule for the line passing through the points (1, 1/4) and (3, 3/4) is y = \frac{1}{4}x .

\textbf{Answer:} y = \frac{1}{4}x