Find the slope and the \( y \)-intercept of the line. \( y=\frac{1}{4} x \) slope: \( y \)-intercept: \( \square \)

To determine the slope and the \( y \)-intercept of the line given by the equation: \[ y = \frac{1}{4}x \] we can compare it to the slope-intercept form of a linear equation: \[ y = mx + b \] where: - \( m \) is the **slope** of the line. - \( b \) is the **\( y \)-intercept**, the point where the line crosses the \( y \)-axis. **1. Finding the Slope (\( m \)):** In the equation \( y = \frac{1}{4}x \), the coefficient of \( x \) is \( \frac{1}{4} \). This coefficient represents the slope of the line. \[ \text{slope} = \frac{1}{4} \] **2. Finding the \( y \)-Intercept (\( b \)):** The equation can be rewritten to explicitly show the \( y \)-intercept by comparing it to the slope-intercept form: \[ y = \frac{1}{4}x + 0 \] Here, the constant term is \( 0 \), which means the line crosses the \( y \)-axis at the origin. \[ y\text{-intercept} = 0 \] **Final Answer:** \[ \boxed{ \begin{aligned} \text{slope: } & \frac{1}{4} \\ y\text{-intercept: } & 0 \end{aligned} } \]