**Finding the Equation of the Tangent Line to a Graph**To find the equation for the line tangent to the graph of the function \[ f(x) = \frac{2x}{x + 4} \]at the point \((2, 0.66666666666667)\).Below the instruction, there is an empty input box where students can input the equation of the tangent line in the form \( y = \).### Explanation:1. **Identify the Function**: The function given is \( f(x) = \frac{2x}{x + 4} \).2. **Given Point on the Graph**: The point at which the tangent line is to be found is \((2, 0.66666666666667)\).3. **Objective**: Find the equation of the tangent line to the graph of \( f(x) \) at the given point.### Steps to Find the Tangent Line Equation:1. **Find the derivative of the function** \( f(x) \) to determine the slope of the tangent line.2. **Evaluate the derivative at \( x = 2 \) to find the slope at the given point**.3. **Use the point-slope form of the equation of a line**:\[ y - y_1 = m(x - x_1) \]where \( (x_1, y_1) \) is the point \((2, 0.66666666666667)\) and \( m \) is the slope found in step 2.### Input Your Answer:Students will input their final equation for the tangent line in the designated box provided. ---This structured explanation helps guide learners through the process of finding the tangent line step-by-step.

Name: **Finding the Equation of the Tangent Line to a Graph**To find the eq
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: **Finding the Equation of the Tangent Line to a Graph**To find the equation for the line tangent to the graph of the function \[ f(x) = \frac{2x}{x + 4} \]at the point \((2, 0.66666666666667)\).Below the instruction, there is an empty input box wher