To find the equation of a line with a slope of 1 that passes through the point (5, 3), we can use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope, and \( (x_1, y_1) \) is the point on the line.
Here, the slope \( m = 1 \) and the point \( (x_1, y_1) = (5, 3) \).
Plugging in these values into the equation:
\[ y - 3 = 1(x - 5) \]
Simplifying this:
\[ y - 3 = x - 5 \] \[ y = x - 5 + 3 \] \[ y = x - 2 \]
So the equation of the line is:
\[ y = x - 2 \]
From the options provided, the correct answer is:
y = x - 2.