Question 8 of 16 Step 1 of 1
Find the equation of a tangent line to the graph of the function that is parallel to the line . If there is no solution, write
None for your answer.

To find the equation of a tangent line to the graph of the function that is parallel to the line , we first note that a parallel line will have the same slope as the line given. The slope of the line is .

Next, we need to derive to find the slope of the tangent line. The derivative is given by:

We set this equal to the desired slope:

Solving for :

Now that we have , we can find the corresponding -coordinate by substituting back into :

Thus, the point of tangency is . Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:

Distributing gives us:

So, the equation of the tangent line to the graph of that is parallel to the line is