Final answer:
The equation of the line that is parallel to the given line y = 1/2x + 8 and that passes through the point (-6,4) is y = 1/2x + 7.
Step-by-step explanation:
The student is seeking the equation of a line that is parallel to a given line and passes through a particular point. The given line is y = ½x + 8, and the line that is parallel to it must have the same slope, which is ½ in this case. Since the line must go through the point (-6,4), we can use the point-slope form to find the equation of the desired line:
y - y1 = m(x - x1)
Substituting the point (-6,4) and the slope ½ yields:
y - 4 = ½(x + 6)
Expanding and simplifying, we get:
y = ½x + 3 + 4
y = ½x + 7
Therefore, the equation of the line parallel to the given line and passing through the point (-6,4) is y = ½x + 7.