Final answer:
To find the equation of a line perpendicular to y=1/3x and passing through the point (1, -2), we use the point-slope form of a linear equation.
Step-by-step explanation:
To find an equation that is perpendicular to y = 1/3x and passes through the point (1, -2), we first need to determine the slope of the given line. The slope of the line y = 1/3x is 1/3. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the perpendicular line will be -3. Now we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The equation will be y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.
Substituting the values, we have y - (-2) = -3(x - 1). Simplifying, we get y + 2 = -3x + 3. Rearranging the equation, we have y = -3x + 1. Therefore, the equation that passes through the point (1, -2) and is perpendicular to y = 1/3x is y = -3x + 1.