Final answer:
The equation of the line that is perpendicular to y=2x+1 and passes through the point (8,11) is y=-1/2x+15.
Step-by-step explanation:
The student is tasked with finding the equation of a line that passes through a specific point and is perpendicular to another given line. The equation of the given line is y = 2x + 1, which means the slope (m) is 2. For a line to be perpendicular, its slope must be the negative reciprocal of the given line's slope. Therefore, the slope of the perpendicular line would be -1/2.
To find the equation of the line passing through a point (8,11), we use the point-slope formula y - y1 = m(x - x1) where (x1, y1) is the point the line passes through, and m is the slope of the line. Substituting the point (8,11) and the slope -1/2 into the formula yields: y - 11 = (-1/2)(x - 8). Expanding and rearranging, we get the equation of the desired line: y = -1/2x + 15.