Final answer:
The equation of a line that is parallel to x-4y=12 and passes through the point (8,8) is y = ¼x + 6.
Step-by-step explanation:
To find the equation of a line that is parallel to another line, you must ensure that both lines have the same slope. The given equation, x - 4y = 12, can be rewritten in slope-intercept form as y = ¼x - 3, which reveals a slope (m) of ¼. To get the equation of the line that passes through (8,8) and is parallel to the original line, use the point-slope form of a line equation, y - y1 = m(x - x1), where (x1, y1) is (8,8) and m is ¼. After substituting the values, the equation will be y - 8 = ¼(x - 8). Simplifying this, we get y = ¼x + 6 as the equation of the desired line.