Final answer:
To find the equation of a line that is perpendicular to another line, use the negative reciprocal of the slope of the given line and the point-slope form of a linear equation. Final equation: y = (1/3)x + 3
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of -3, so the perpendicular line will have a slope of 1/3. Let's use the point-slope form of a linear equation to find the equation of the perpendicular line.
Given point: (6, 5)
Slope of the perpendicular line: 1/3
Equation of the line: y - y1 = m(x - x1)
Substituting the values, we get: y - 5 = (1/3)(x - 6)
Simplifying, we get: y - 5 = (1/3)x - 2
Final equation: y = (1/3)x + 3