Final answer:
The line parallel to y = -3/4x + 1 that contains the point (8,1) has the same slope of -3/4. By testing both options with the same slope, we find that y = -3/4x + 7 is the correct equation that includes the point (8,1).
Step-by-step explanation:
To find a line parallel to the given line y = -3/4x + 1, we need a line with the same slope since parallel lines have equal slopes. The slope of the given line is -3/4. Therefore, our new equation must have the slope -3/4 as well. Among the given options, both Option 1 (y = -3/4x + 7) and Option 3 (y = -3/4x - 7) have the same slope. To determine which of these two options contains the point (8,1), we can substitute these x and y values into both equations to see if they satisfy the equation.
For Option 1: 1 = -3/4(8) + 7 which simplifies to 1 = -6 + 7. This is true, so Option 1 is a possible solution.
For Option 3: 1 = -3/4(8) - 7 which simplifies to 1 = -6 - 7. This is false, so Option 3 is not the correct equation.
Therefore, the equation that represents a line parallel to the line y = -3/4x + 1 and contains the point (8,1) is Option 1: y = -3/4x + 7.