Final answer:
To find the line parallel to y = 1/4x + 1 that passes through the point (6, -2), we can use the point-slope form of a linear equation. Plugging in the values (6, -2) and the slope 1/4 into the equation, we obtain the equation of the parallel line y = 1/4x - 7/2.
Step-by-step explanation:
To find the line parallel to y = 1/4x + 1 that passes through the point (6, -2), we need to find a line with the same slope. The slope of y = 1/4x + 1 is 1/4, so the parallel line will also have a slope of 1/4. Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values of the point and slope to obtain the equation of the parallel line. Plugging in the values (6, -2) and 1/4 into the equation, we get y - (-2) = 1/4(x - 6), which simplifies to y + 2 = 1/4x - 3/2. Finally, rearranging this equation to slope-intercept form, we have y = 1/4x - 3/2 - 2, which simplifies to y = 1/4x - 3/2 - 4/2, resulting in y = 1/4x - 7/2, option c.