The slope of the tangent line is the coefficient of x in the equation, which is 1/21 in this case.
To find the equation of a tangent line, you need to know the slope of the tangent line and a point on the line. In this case, the slope is 1/21 and the point is (0, 6/7). You can then use the point-slope formula to find the equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. This will give you the equation y = 1/21x + 6/7.
The tangent line represents the instantaneous rate of change of a function at a specific point. It is used in calculus to find the derivative of a function, which is a fundamental concept in understanding the behavior and properties of functions.
Yes, the equation of the tangent line can change depending on the point on the curve where it is drawn. The slope of the tangent line will also change if the function itself is changing at that point.
The equation of a tangent line is directly related to the derivative of a function. The derivative of a function at a specific point is equal to the slope of the tangent line at that point. This is why the tangent line is used to find the derivative and vice versa.