Final answer:
The equation of a line parallel to y=3x+7 that passes through (1,8) is y=3x+5. This is achieved by maintaining the same slope as the original line, which is 3, and solving for the y-intercept using the given point.
Step-by-step explanation:
To find the equation of a line that is parallel to y=3x+7 and passes through the point (1,8), we must use the fact that parallel lines have the same slope. The given line has a slope of 3, so our new line will also have a slope of 3. To find the y-intercept (b) of our new line, we use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through, and m is the slope.
Plugging our point and slope into the equation, we get y - 8 = 3(x - 1). Simplify to find y: y - 8 = 3x - 3, and then add 8 to each side: y = 3x + 5.
Therefore, the equation of the line parallel to y=3x+7 that passes through (1,8) is y=3x+5, which corresponds to option A) y=3x+5.