Final answer:
To find the equation of a line perpendicular to y= 3/2x+1 and passing through the point (5,1), we need to find the negative reciprocal of the slope of the given line. The slope of the perpendicular line is -2/3. Using the point-slope form of a line, we can find the equation of the perpendicular line as y = -2/3x + 11/3.
Step-by-step explanation:
To find the equation of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of 3/2, so the negative reciprocal of 3/2 is -2/3. Therefore, the slope of the perpendicular line is -2/3.
Next, we can use the point-slope form of a line to find the equation of the perpendicular line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Since the perpendicular line passes through the point (5,1), we can substitute x1 = 5 and y1 = 1 into the point-slope form. This gives us y - 1 = -2/3(x - 5). Simplifying the equation further, we get the equation of the perpendicular line as y = -2/3x + 11/3.