Q. Find the slope of the line \(y = 12x + \tfrac{1}{6}\).

1. Recognize the form of the equation.

   The slope-intercept form of a line is given by \(y = mx + b\), where \(m\) denotes the slope and \(b\) denotes the y-intercept. When an equation is written in this form, the coefficient of \(x\) is the slope.

2. Write down the given equation.

   The line is \(y = 12x + \tfrac{1}{6}\).

3. Identify the slope from the equation.

   Comparing \(y = 12x + \tfrac{1}{6}\) with \(y = mx + b\), the coefficient of \(x\) is \(m = 12\). Therefore the slope is 12.

4. (Optional) Verify by using two points and the rise-over-run formula.

   Choose two x-values, for example \(x_1 = 0\) and \(x_2 = 1\).

   Compute corresponding y-values:

   \(y_1 = 12(0) + \tfrac{1}{6} = \tfrac{1}{6}\), so the point is \((0,\tfrac{1}{6})\).

   \(y_2 = 12(1) + \tfrac{1}{6} = 12 + \tfrac{1}{6} = \tfrac{73}{6}\), so the point is \((1,\tfrac{73}{6})\).

   Compute the slope using rise over run:

   \(m = \dfrac{y_2 – y_1}{x_2 – x_1} = \dfrac{\tfrac{73}{6} – \tfrac{1}{6}}{1 – 0} = \dfrac{\tfrac{72}{6}}{1} = \dfrac{12}{1} = 12\).

   This confirms the slope is 12.

Answer: The slope of the line is 12.