Final answer:
To write the equation of the line parallel to y = 1/4x + 5 and passing through point P(4, 8), use the slope 1/4 from the given line and apply point-slope form resulting in the equation y = 1/4x + 6.
Step-by-step explanation:
The student is asked to write an equation of a line that is parallel to another given line and passes through a specific point. Since parallel lines have the same slope, we can use the slope of the given line y = 1/4x + 5, which is 1/4, for our new line. Using the point-slope form of the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Substituting the point P(4, 8) and the slope 1/4 into the point-slope equation, we get:
y - 8 = 1/4(x - 4)
Now, we simplify and put it in the slope-intercept form y = mx + b where m is the slope and b is the y-intercept:
y = 1/4x + 6
This is the equation of the line that is parallel to line K and passes through point P(4, 8).