Find the \( x \) - and \( y \)-intercepts of the graph of \( x-3 y=7 \). State each answer as an or an improper fraction in simplest form.

To find the \( x \)- and \( y \)-intercepts of the equation \( x - 3y = 7 \), follow these steps: ### \( x \)-Intercept: The \( x \)-intercept occurs where \( y = 0 \). 1. Substitute \( y = 0 \) into the equation: \[ x - 3(0) = 7 \implies x = 7 \] 2. So, the \( x \)-intercept is \( \left( \frac{7}{1},\ 0 \right) \). ### \( y \)-Intercept: The \( y \)-intercept occurs where \( x = 0 \). 1. Substitute \( x = 0 \) into the equation: \[ 0 - 3y = 7 \implies -3y = 7 \implies y = -\frac{7}{3} \] 2. So, the \( y \)-intercept is \( \left( 0,\ -\frac{7}{3} \right) \). ### Summary of Intercepts: - **\( x \)-Intercept:** \( \left( \frac{7}{1},\ 0 \right) \) - **\( y \)-Intercept:** \( \left( 0,\ -\frac{7}{3} \right) \)