To find the x- and y-intercepts of the line given by the equation \( y = -5x + \frac{1}{3} \), we can follow these steps:
Y-Intercept
The y-intercept occurs when \( x = 0 \).
- Substitute \( x = 0 \) into the equation: \[ y = -5(0) + \frac{1}{3} = \frac{1}{3} \] So, the y-intercept is at the point \( (0, \frac{1}{3}) \).
X-Intercept
The x-intercept occurs when \( y = 0 \).
- Set \( y = 0 \) and solve for \( x \): \[ 0 = -5x + \frac{1}{3} \] \[ 5x = \frac{1}{3} \] \[ x = \frac{1}{3 \cdot 5} = \frac{1}{15} \] So, the x-intercept is at the point \( \left( \frac{1}{15}, 0 \right) \).
Summary
- The y-intercept is \( (0, \frac{1}{3}) \).
- The x-intercept is \( \left( \frac{1}{15}, 0 \right) \).