If a line has an \( x \)-intercept at \( x=4 \) and a \( y \)-intercept at \( y=-1 \), find its equation in the form \( y=m x+b \). \( y=\square \)

To find the equation of the line in the form \( y = mx + b \), we can start by identifying the \( x \)-intercept and \( y \)-intercept. The \( x \)-intercept at \( x=4 \) means the line crosses the x-axis at the point \( (4, 0) \). The \( y \)-intercept at \( y=-1 \) tells us the line crosses the y-axis at the point \( (0, -1) \). Now, we can calculate the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-1)}{4 - 0} = \frac{1}{4}. \] Using the slope and the \( y \)-intercept to write the equation, we have: \[ y = \frac{1}{4} x - 1. \] Thus, the equation of the line is: \( y = \frac{1}{4} x - 1 \).