Final answer:
The equations of the lines are y = -3x + 1 and y = (1/2)x - 6.
Step-by-step explanation:
To find the equations of the lines, we need to determine the slope and y-intercept of each line.
The slope of a line is determined by the change in y divided by the change in x. Using the given points (0,1) and (2,-5), the slope of the first line is (1-(-5))/(0-2) = 6/(-2) = -3.
Using the given points (0,-6) and (2,-5), the slope of the second line is (-6-(-5))/(0-2) = -1/(-2) = 1/2.
The y-intercept of each line can be found by substituting the slope and one of the given points into the equation y = mx + b, where m is the slope and b is the y-intercept.
For the first line with slope -3, substituting (0,1) gives 1 = -3(0) + b, which simplifies to b = 1.
For the second line with slope 1/2, substituting (0,-6) gives -6 = (1/2)(0) + b, which simplifies to b = -6.
Therefore, the equations of the lines are y = -3x + 1 and y = (1/2)x - 6.