Question

Find the equation of a line that is perpendicular to (y = {1}/{2}) and passes through the point (3,2). Give your answer in the form (y = mx + ).

a) (y = -2x + 8)
b) (y = 2x + 8)
c) (y = -2x - 8)
d) (y = 2x - 8)

Answer 1

The equation of a line perpendicular to a line with a slope of 1/2 and passing through the point (3,2) is y = -2x + 8.

Step-by-step explanation:

The equation y = 1/2 represents a horizontal line, which means its slope is 0. A line that is perpendicular to a horizontal line is a vertical line, which has an undefined slope. However, based on the context provided, it seems that we are actually looking for the equation of a line perpendicular to a line with a slope of 1/2, not the equation y = 1/2 itself. Hence, the slope of the perpendicular line should be the negative reciprocal of 1/2, which is -2.

To write the equation of this line in slope-intercept form, y = mx + b, we substitute the slope (-2) and use the point (3,2) to solve for the y-intercept b. Plugging in (3,2):

2 = -2(3) + b

This simplifies to:

2 = -6 + b

Then, by adding 6 to both sides, we find:

b = 8

Therefore, the equation of our line is: y = -2x + 8, which corresponds to option a).