Final answer:
The equation of the line parallel to y = 2/3x - 6 that passes through (9, -3) is y = 2/3x - 9, found by using the point-slope form and the given point.
Step-by-step explanation:
The student is asking for the equation of a line that is parallel to the given line y = ⅓x - 6 and that passes through a specific point, which in this case is (9, -3). To find this equation, you need to understand that parallel lines have the same slope. Since the given line has a slope of ⅓, the line we want to find will also have this slope. Using the point-slope form of the equation of a line, y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passes through, we can plug in our slope of ⅓ and our point (9, -3) to find the specific equation.
When we do this, we get the equation: y + 3 = ⅓(x - 9). Simplifying this, we multiply the right side out to get ⅓x - 6, and then add 3 to both sides to isolate y, resulting in y = ⅓x - 9, which is the equation of the desired line.