Final answer:
To find the equation of a line that is perpendicular to the line y = (1/2)x + 2 and passes through the point (5, 2), the slope of the perpendicular line is -2. The equation of the line is y = -2x + 12.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the line y = (1/2)x + 2 and passes through the point (5, 2), we need to determine the slope of the perpendicular line. The given line has a slope of (1/2), so the perpendicular line will have a slope that is the negative reciprocal of (1/2). Therefore, the slope of the perpendicular line is -2.
Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope (-2) and the coordinates of the point (5, 2) into the equation to find the value of b.
2 = -2(5) + b
2 = -10 + b
b = 12
So the equation of the line that is perpendicular to y = (1/2)x + 2 and passes through the point (5, 2) is y = -2x + 12.