Final answer:
The equation of the line perpendicular to the given line x-2y = 2 and passing through the point (-5,2) is y = -2x - 8.
Step-by-step explanation:
The student is asking for the equation of a line that is perpendicular to a given line and passes through a specific point. First, we need to find the slope of the given line by transforming its equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. For the line x - 2y = 2, rewriting it in slope-intercept form gives us y = (1/2)x - 1.
Therefore, the slope is 1/2. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line we are looking for is -2.
We can now use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through, and m is the slope. Substituting the point (-5, 2) and the slope -2, we get y - 2 = -2(x + 5). Simplifying, we have the perpendicular line's equation: y = -2x - 8.