We take the derivative implicitly: Substitute (x,y) = (4,1) The derivative at a point is the slope of the line tangent to the curve at the point, therefore the slope of the tangent line is We use the point-slope formula for the equation of the tangent line: where (x1,y1) = (4,1) [Do not substitute for x and y, but leave them as variables] , graphed in green below: Edwin