Final answer:
To find the equation of a line perpendicular to y = 1/2x + 5 that contains a given point, we first determine the negative reciprocal of the slope of the given line. Then, we use the point-slope form of a linear equation to find the equation of the line using the given point and the negative reciprocal slope. The equation of the line perpendicular to y = 1/2x + 5 that contains point P(7, -2) is y = -2x + 12.
Step-by-step explanation:
To find the equation of a line perpendicular to y = 1/2x + 5, we first need to determine the slope of the given line. The slope of the given line is 1/2, so the slope of the perpendicular line would be the negative reciprocal. The negative reciprocal of 1/2 is -2.
Next, we can use the point-slope form of a linear equation to find the equation of the line. We have the point P(7, -2) and the slope -2. Plugging these values into the point-slope form equation, we get y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point.
Substituting the values, we get y - (-2) = -2(x - 7). Simplifying the equation gives us y + 2 = -2x + 14. Finally, rearranging the equation gives us the equation of the perpendicular line as y = -2x + 12.