To find the x- and y-intercepts of the line given by the equation \( y = -9x - \frac{9}{8} \), we will follow these steps:
1. Finding the y-intercept: The y-intercept occurs when \( x = 0 \).
Substituting \( x = 0 \) into the equation: \[ y = -9(0) - \frac{9}{8} = -\frac{9}{8} \]
So, the y-intercept is: \[ (0, -\frac{9}{8}) \]
2. Finding the x-intercept: The x-intercept occurs when \( y = 0 \).
Setting \( y = 0 \) and substituting into the equation: \[ 0 = -9x - \frac{9}{8} \]
Now, solve for \( x \): \[ 9x = -\frac{9}{8} \] \[ x = -\frac{9}{8 \cdot 9} = -\frac{1}{8} \]
So, the x-intercept is: \[ (-\frac{1}{8}, 0) \]
Summary of intercepts:
- y-intercept: \( (0, -\frac{9}{8}) \)
- x-intercept: \( (-\frac{1}{8}, 0) \)