Final answer:
To find the equation of the line passing through (1, 2) that is perpendicular to the line through (3, -2) and (-3, 0), use the point-slope form of the equation of a line. Substitute the given point and the negative reciprocal of the given line's slope to find the equation.
Step-by-step explanation:
To find the equation of the line passing through (1, 2) that is perpendicular to the line through (3, -2) and (-3, 0), we first need to find the slope of the given line. The slope of a line can be found using the formula: slope = (y2 - y1)/(x2 - x1). Using this formula, the slope of the given line is: slope = (-2 - 0)/(3 - (-3)) = -1/2. As the given line is perpendicular to the line we need to find, the slope of the perpendicular line will be the negative reciprocal of this slope. So, the slope of the perpendicular line is 2.
Next, we can use the point-slope form of the equation of a line, which is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting (1, 2) as the point and 2 as the slope, we get: y - 2 = 2(x - 1). Simplifying this equation gives us the equation of the line passing through (1, 2) that is perpendicular to the given line: y = 2x.