2.3 Q5) Hey, I need help with the following calc problem. Thank you! # Finding the Equation of a Tangent Line to a Curve## Problem StatementFind an equation of the tangent line to the curve at the given point.\[ y = \frac{(x - 1)}{(x - 2)} \quad \text{at} \quad (3, 2) \]Below the text, a blank rectangle is shown, indicating where additional explanations, calculations, or graphical representations can be added.---### Solution Steps1. **Identify the given function and point:** - Function: \( y = \frac{(x - 1)}{(x - 2)} \) - Point: \( (3, 2) \)2. **Find the derivative \( y' \) of the function to get the slope of the tangent line at the given point.**3. **Evaluate the derivative at \( x = 3 \) to find the slope of the tangent line.**4. **Use the point-slope form of the equation of a line:** - Point-slope form: \( y - y_1 = m(x - x_1) \) - Where \( (x_1, y_1) \) is the given point and \( m \) is the slope.5. **Substitute the values into the point-slope form to find the equation of the tangent line.**---This page provides a step-by-step approach to solve for the equation of the tangent line to the given curve at a specific point, including the necessary differentiation and substitution steps.

Equation of line passing through and whose slope is m is given as

Answered: Find an equation of the tangent line to…

Math

Calculus

Find an equation of the tangent line to the curve at the given point. y = (x - 1)/(x - 2), (3, 2)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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2.3 Q5) Hey, I need help with the following calc problem. Thank you!

# Finding the Equation of a Tangent Line to a Curve

## Problem Statement

Find an equation of the tangent line to the curve at the given point.

\[ y = \frac{(x - 1)}{(x - 2)} \quad \text{at} \quad (3, 2) \]

Below the text, a blank rectangle is shown, indicating where additional explanations, calculations, or graphical representations can be added.

---

### Solution Steps

1. **Identify the given function and point:**
- Function: \( y = \frac{(x - 1)}{(x - 2)} \)
- Point: \( (3, 2) \)

2. **Find the derivative \( y' \) of the function to get the slope of the tangent line at the given point.**

3. **Evaluate the derivative at \( x = 3 \) to find the slope of the tangent line.**

4. **Use the point-slope form of the equation of a line:**
- Point-slope form: \( y - y_1 = m(x - x_1) \)
- Where \( (x_1, y_1) \) is the given point and \( m \) is the slope.

5. **Substitute the values into the point-slope form to find the equation of the tangent line.**

---

This page provides a step-by-step approach to solve for the equation of the tangent line to the given curve at a specific point, including the necessary differentiation and substitution steps.

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