We know that: (1) the radius of the circle to the point [4,3] is perpendicular to the tangent line, (2) if two lines are perpendicular, their gradients are __negative reciprocals__ of each other, and (3) the formula for a straight line is y = mx + c. The radius gradient is equal to *3/4*, so the tangent gradient is *-4/3*. Substituting m, y and x at [4,3] into the straight line formula gives *c* as *25/3*. Therefore, the equation of this tangent line is __y = (-4/3)x + (25/3)__.