Answer:
The equation of the line is
.
Step-by-step 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
.