Line Equation B60409

1. **State the problem:** We need to find the equation of a line in slope-intercept form, which is $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. 2. **Identify given points:** The line passes through points $$(6, 0)$$ and $$(12, 1)$$, and crosses the y-axis at $$-1$$. 3. **Calculate the slope $$m$$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{12 - 6} = \frac{1}{6}$$ 4. **Use the slope-intercept form:** We know $$m = \frac{1}{6}$$ and the y-intercept $$b = -1$$. 5. **Write the equation:** $$y = \frac{1}{6}x - 1$$ 6. **Verify with a point:** Using point $$(6, 0)$$: $$y = \frac{1}{6} \times 6 - 1 = 1 - 1 = 0$$ which matches the point. **Final answer:** $$y = \frac{1}{6}x - 1$$