Step 1 :The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 :The slope of a line parallel to another line is the same as the slope of the original line. Therefore, the slope of line \(u\) is the same as the slope of line \(t\), which is \(-\frac{1}{7}\).
Step 3 :We know that line \(u\) passes through the point \((7,6)\). We can substitute these values into the equation \(y = mx + b\) to find the y-intercept \(b\).
Step 4 :Substituting \(x = 7\), \(y = 6\), and \(m = -\frac{1}{7}\), we get: \(6 = -\frac{1}{7} * 7 + b\)
Step 5 :Solving for \(b\), we get: \(b = 6 + 1 = 7\)
Step 6 :Therefore, the equation of line \(u\) in slope-intercept form is \(\boxed{y = -\frac{1}{7}x + 7}\)