# How do you find the slope of a tangent line?

## How do you find the slope of a tangent line?

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f ‘(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

## What is the equation of the tangent line?

What is the tangent line equation? The equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.

**What is difference between tangent and slope?**

The tangent to a curve at a point is a straight line just touching the curve at that point; the slope of the tangent is the gradient of that straight line.

### Why does the derivative give the slope of a tangent line?

When you plug in an x-value into a function’s derivative, the y-values you get back FROM THE DERIVATIVE tell you the slope of a tangent line to the original function at that value of x.

The formal definition of the limit can be used to find the slope of the tangent line: If the point P (x0,y0) is on the curve f, then the tangent line at the point P has a slope given by the formula: Mtan = lim h→0 f (x0 + h) – f (x0)/h.

### What does the slope of the tangent line tell us?

The slope of a position-versus-time graph represents the velocity. Explanation: The slope of the tangent line represents the rate of change of a function. Velocity is the rate of change of position with respect to time. Equivalently, velocity is the derivative of the position function.

**Can you find equations of the tangent lines?**

Method 1 of 2: Finding the Equation of a Tangent Line Sketch the function and tangent line (recommended). A graph makes it easier to follow the problem and check whether the answer makes sense. Take the first derivative to find the equation for the slope of the tangent line. [1] … Enter the x value of the point you’re investigating. Write the tangent line equation in point-slope form.

## How to determine the tangent line at a curve?

Finding the equation of a line tangent to a curve at a point always comes down to the following three steps: Find the derivative and use it to determine our slope m at the point given Determine the y value of the function at the x value we are given. Plug what we’ve found into the equation of a line.