Determine the point-slope form of a line passing through the points \( (1, 2) \) and \( (3, 8) \).

To find the point-slope form of a line passing through the points \( (1, 2) \) and \( (3, 8) \), we first need to calculate the slope (\( m \)) of the line. The slope formula is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in our points \( (x_1, y_1) = (1, 2) \) and \( (x_2, y_2) = (3, 8) \): \[ m = \frac{8 - 2}{3 - 1} = \frac{6}{2} = 3 \] Now that we have the slope, we can use the point-slope form equation, which is: \[ y - y_1 = m(x - x_1) \] Choosing point \( (1, 2) \): \[ y - 2 = 3(x - 1) \] This is the point-slope form of the line. Expanding it will give you: \[ y - 2 = 3x - 3 \implies y = 3x - 1 \] So, the point-slope form is \( y - 2 = 3(x - 1) \).