Find the slope and \( y \)-intercept of the following linear equation. Express the \( y \)-intercept as a coordinate pair. \[ y=\frac{1}{5} x \] Answer

To identify the slope and \( y \)-intercept of the linear equation: \[ y = \frac{1}{5}x \] we can compare it to the standard slope-intercept form of a linear equation: \[ y = mx + b \] where: - \( m \) is the **slope** of the line. - \( b \) is the **\( y \)-intercept**, expressed as a coordinate pair \((0, b)\). **Step-by-Step Breakdown:** 1. **Identify the Slope (\( m \)):** In the given equation, \( y = \frac{1}{5}x \), the coefficient of \( x \) is \( \frac{1}{5} \). \[ \text{Slope } (m) = \frac{1}{5} \] 2. **Determine the \( y \)-Intercept (\( b \)):** The equation \( y = \frac{1}{5}x \) does not have a constant term, which implies that \( b = 0 \). Therefore, the \( y \)-intercept is at the point where \( x = 0 \): \[ y = \frac{1}{5}(0) = 0 \] \[ \text{\( y \)-intercept} = (0, 0) \] **Final Answer:** - **Slope:** \( \frac{1}{5} \) - **\( y \)-intercept:** \( (0,\,0) \)