To find the slope and y-intercept of the line defined by the equation ax + by = 0, we need to rearrange this equation into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let’s rearrange the equation:
- Start with the original equation: ax + by = 0.
- Isolate y by moving ax to the right side: by = -ax.
- Now, divide every term by b (assuming b ≠ 0): y = - rac{a}{b} x.
In this form, we can see that the slope m is - rac{a}{b} and the y-intercept b (where the line crosses the y-axis) is 0 because there is no constant term added.
In conclusion, the slope of the line ax + by = 0 is - rac{a}{b} and the y-intercept is (0, 0).