Final answer:
To find the equation of a parallel line to y = (1/3)x - 5 that passes through (3, 2), one must use the same slope of 1/3 and apply the point-slope form to get the new line's equation y = (1/3)x + 1.
Step-by-step explanation:
The student's question is about finding the equation of a line that is parallel to a given line y = (1/3)x - 5, and that passes through a specific point (3, 2). Since parallel lines have the same slope, we will use the same slope of (1/3) from the given line for our new line's equation. We use the point-slope form of a line which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Since we know the slope m is (1/3) and our line passes through (3, 2), we can substitute these values into the point-slope formula:
y - 2 = (1/3)(x - 3)
Distributing the (1/3), we get:
y - 2 = (1/3)x - 1
Then, we add 2 to both sides to solve for y:
y = (1/3)x + 1
This is the equation of the parallel line that passes through the point (3, 2). The process involves finding the slope of the parallel line, using the point-slope form, and then rearranging the equation to the slope-intercept form (y = mx + b).