Q. 62 - Calculus

Question

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line tangent to the graph of $y=4 x+3$ at the point $(-2,-5)$

Step-by-Step Solution

Answer

The equation of tangent line is $y=-5x-15$

Step 1. Given information

Given function $y=4x+3$ and the point $(-2,-5)$

Step 2: Calculate the derivative at the point

Calculating, we get

$$\begin{gathered} y=4x+3 \\ y\text{'}(-2,-5)=4(-2)+3 \\ y\text{'}(-2,-5)=-5 \end{gathered}$$

Step 3: Use the point slope form to get the equation

Calculating, we get

$$\begin{gathered} y+5=-5(x+2) \\ y+5=-5x-10 \\ y=-5x-15 \end{gathered}$$