Final answer:
The equation of the line perpendicular to y=2x+6 and passing through the point (4,5) is y=(-1/2)x+7.
Step-by-step explanation:
The question involves finding the equation of a line that is perpendicular to a given line and passes through a specific point. Given the equation y=2x+6, we know the slope of this line is 2. A line perpendicular to this would have a slope that is the negative reciprocal, which is -1/2. Using the point-slope form (y - y1) = m(x - x1), where (x1, y1) is the point (4,5), we can substitute the slope and the point to get:
y - 5 = (-1/2)(x - 4)
To write this in slope-intercept form, we need to distribute the slope and add 5 to both sides:
y = (-1/2)x + 7
This equation represents the desired line that is perpendicular to y=2x+6 and crosses through (4,5).