it should probably be in slope-intercept formkdpointer said:Thus the final equation is y-8 = 7x ?
kdpointer said:It says that point-slope form is fine.. but it would be y=7x+8
The equation of the tangent line to a curve at a given point is given by the point-slope form: y - y1 = m(x - x1), where m is the slope of the tangent line and (x1, y1) is the given point on the curve.
The slope of the tangent line to a curve can be calculated using the derivative of the curve at the given point. The derivative represents the slope of the tangent line at any point on the curve.
Yes, the equation of the tangent line to a curve can change at different points because the slope of the tangent line is dependent on the derivative, which can vary at different points on the curve.
No, the tangent line is not always perpendicular to the curve at the point of tangency. This only occurs when the curve is a circle or has a circular shape.
The equation of the tangent line to a curve is used in various real-world applications, such as physics, engineering, and economics. It helps in determining the instantaneous rate of change of a variable and can be used to predict future behavior of a system.