How do you find the equation of a tangent?

To find the equation of a tangent, first, find the gradient of the radius, for example, if the radius went from the origin to (3,4), the gradient would be 4-0/3-0 =4/3 because the gradient = change in y/ change in x. Then find the gradient of the tangent by taking the negative reciprocal of the first gradient which is – 3/4, Now complete the rest of the equation, as the straight-line equation is y = -3/4x + c, and as y = 4 and x = 3, this = 4 = -9/4 + c, and as 25 the diameter, y = -3/4x + 25/4