Final answer:
To find the equation of a line perpendicular to x - 2y = 4, we determine the slope of the given line, which is 1/2, and then use the negative reciprocal for the slope of the perpendicular line, resulting in a slope of -2. Thus, the equation is y = -2x + b, where b is the y-intercept.
Step-by-step explanation:
The equation of a line that is perpendicular to the line given by x - 2y = 4 can be found by first determining the slope of the given line. To put the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we rearrange the equation as follows:
- x - 2y = 4
- -2y = -x + 4
- y = (1/2)x - 2
The slope of the given line is 1/2. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. Thus, the slope of the perpendicular line is -2. Using the slope-intercept form, the equation of a line with slope -2 and an arbitrary y-intercept b, which is not determined without an additional point, is y = -2x + b.