Final answer:
The equation of the line that is perpendicular to the line 8x + 4y = 8 and passes through the point (2, 6) is y = (1/2)x + 5.
Step-by-step explanation:
The question requires us to find the equation of a line that is perpendicular to the given line 8x + 4y = 8 and that passes through the point (2, 6).
First, we need to find the slope of the given line by rewriting the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
The given line in slope-intercept form is y = -2x + 2, which tells us the slope is -2. A line that is perpendicular to another line has a slope that is the negative reciprocal of the original line's slope.
Therefore, our new line will have a slope of 1/2.
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we plug in our known values to get the equation of our new line: y - 6 = (1/2)(x - 2).
Simplifying, we get the final equation of the perpendicular line: y = (1/2)x + 5.