Final answer:
The equation for the line with a slope of 1/2 and containing the point (0,-1) in standard form is x - 2By + 2B = 0.
Step-by-step explanation:
The equation for a line in standard form is Ax + By = C, where A, B, and C are constants. To find the equation for the line with a slope of 1/2 and containing the point (0,-1), we can substitute the given values into the equation.
First, plug in the slope (m) into the equation: 1/2 = A.
Next, substitute the x and y values from the given point into the equation: 0A + B(-1) = C. Simplify this equation to: -B = C.
Combining the two equations, we have: 1/2x - By = -B.
To convert this equation to standard form, multiply all terms by 2 to get: x - 2By = -2B.
Rearrange the equation to have the constants on the right side: x - 2By + 2B = 0.
Therefore, the equation for the line in standard form is x - 2By + 2B = 0.