What is the equation of the line that passes through the point $(5,8)$ and has a slope of 1 ?

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 ：We know the slope \(m\) is 1, and we know that the line passes through the point \((5,8)\). We can substitute these values into the equation to solve for \(b\).

Step 3 ：Substituting \(m = 1\) and \((x, y) = (5, 8)\) into the equation \(y = mx + b\), we get \(8 = 5 + b\).

Step 4 ：Solving for \(b\), we find that \(b = 3\).

Step 5 ：Substituting \(m = 1\) and \(b = 3\) back into the equation \(y = mx + b\), we get the equation of the line: \(y = x + 3\).

Step 6 ：\(\boxed{y = x + 3}\) is the equation of the line that passes through the point \((5,8)\) and has a slope of 1.