Final answer:
No existing line can pass through point (0,-1) according to the given equation 6x + 6y = 1.
Step-by-step explanation:
To find the equation of the line in slope-intercept form that passes through the point (0,-1), you should first rearrange the given equation (6x + 6y = 1) into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
So, divide the entire equation by 6, resulting in x + y = 1/6. Then, move x to the other side of the equation to get y = -x +1/6.
Because the line passes through (0,-1), substitute these values into the equation -1 = 0 - 1/6. As you can see, -1 does not equal -1/6. Therefore, there has been a mistake in the original question, or we have misunderstood it, as no line that passes through the point (0,-1) can be given by the original equation 6x + 6y = 1.
Learn more about Slope-Intercept Form