The equation of the line perpendicular to y=-1/3x+2 that passes through the point (4,2) is y = 3x - 10. The slope of the perpendicular line is the negative reciprocal of the original line's slope, which is 3. The point-slope form is used to determine the final equation.
The student asked what the equation of the line is that is perpendicular to y=-1/3x+2 and passes through the point (4,2). To find the equation of a line perpendicular to another, we need to determine the perpendicular slope. If a line has a slope m, a line perpendicular to it will have a slope of -1/m. The original line has a slope of -1/3, so the perpendicular line will have a slope of 3.
We use the point-slope formula to find the equation of the perpendicular line: y - y1 = m(x - x1), where (x1, y1) is the given point through which the line passes and m is the slope. Substituting the given point (4,2) and the slope 3, we get y - 2 = 3(x - 4). Simplifying this, we get y = 3x - 10. Therefore, the equation of the perpendicular line is y = 3x - 10.