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. We are given that the slope \(m = 7\) and the line passes through the point \((4,34)\). We can substitute these values into the equation to solve for \(b\).
Step 2 :Substitute \(m = 7\) and \((x, y) = (4, 34)\) into the equation \(y = mx + b\) to get \(34 = 7*4 + b\).
Step 3 :Solve the equation for \(b\) to get \(b = 6\).
Step 4 :\(\boxed{y = 7x + 6}\) is the final answer.