To find the x- and y-intercepts of the line given by the equation \( x + 4y = 36 \), we can follow these steps:
Finding the x-intercept:
The x-intercept occurs when \( y = 0 \). So, we substitute \( y = 0 \) into the equation:
\[ x + 4(0) = 36 \] \[ x = 36 \]
Therefore, the x-intercept is \( (36, 0) \).
Finding the y-intercept:
The y-intercept occurs when \( x = 0 \). So, we substitute \( x = 0 \) into the equation:
\[ 0 + 4y = 36 \] \[ 4y = 36 \] \[ y = \frac{36}{4} = 9 \]
Therefore, the y-intercept is \( (0, 9) \).
Summary:
- The x-intercept is \( (36, 0) \).
- The y-intercept is \( (0, 9) \).