Answer:
The equation of the line is .
Explanation:
Let the function be and the line be . First, we transform the equation of the line into explicit form:
(1)
By Differential Calculus, the slope at any point of the function is represented by its first derivative, that is:
(2)
If the line tangent to the function must be parallel to , then . In consequence, we clear in (2):
Then, we evaluate the function at the result found above to determine the associated value of :
By Analytical Geometry we know that an equation of the line can be formed by knowing both slope () and y-intercept (). If we know that , and , then the y-intercept of the equation of the line is:
Based on information found previously and the equation of the line, we have the equation of the line that is tanget to the graph of , so that it is parallel to is:
The equation of the line is .