Question

Find the x- and y-intercepts of the line y=–5x+1/3
.

Answer 1

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 \( x = 0 \).

1. 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 \( y = 0 \).

1. 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 \( \left( \frac{1}{15}, 0 \right) \).