Question

Write an equation for the line perpendicular to y = 2x - 5 that contains (-9, 6).

A. y - 6 = -1/2(x + 9)
B. y - 9 = -1/2(x + 6)
C. x - 6 = 2(y + 9)
D. y - 6 = 2(x + 9)

Answer 1

The correct equation of the line perpendicular to y = 2x - 5 that contains the point (-9, 6) is A. y - 6 = -1/2(x + 9), using the point-slope form and the negative reciprocal of the given line's slope.

Step-by-step explanation:

We are looking to write an equation for a line that is perpendicular to the given line y = 2x - 5 and passes through the point (-9,6). The slope of the given line is 2, therefore, the slope of the perpendicular line will be its negative reciprocal, which is -1/2. Using the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes, we can substitute the slope and the point to find the equation of the perpendicular line.

Plugging in the values gives us: y - 6 = -1/2(x + 9). This matches option A. Thus, the correct equation of the line perpendicular to y = 2x - 5 that contains the point (-9, 6) is given by A. y - 6 = -1/2(x + 9).