Final answer:
The equation of the reflected line is y = x + 5.
Step-by-step explanation:
The equation of the line formed when the line y = 3x + 1 is reflected in the line y = x can be found by first finding the equation of the line y = x.
The equation of the line y = x represents a line that passes through the origin with a slope of 1.
To reflect the line y = 3x + 1 in the line y = x, we need to find the reflection of each point on the line y = 3x + 1 across the line y = x.
This can be done by finding the line that is parallel to y = x and passes through each point on the line y = 3x + 1.
The equation of this reflected line can be found by using the point-slope form of a line.
Let's take a point on the line y = 3x + 1, for example, (2, 7).
To find its reflection across the line y = x, we can use the point-slope form of a line with the slope of 1 and the point (2, 7). Plugging these values into the point-slope form, we get: y - 7 = 1(x -2).
Simplifying this equation, we get: y = x + 5.
Therefore, the equation of the line formed when the line y = 3x + 1 is reflected in the line y = x is y = x + 5.