Step-by-step explanation:
Exponential function is given by general form 
Where a and b are constants.
say a=1 and b=2 then we can write function as :

or 
To graph this or any exponential function, we just need to find some points then join them by a curved line.
Like plug x=0, 1, 2,... into above function and find points:
plug x=1

Hence point is (1,2)
Find more points similarly then graph them to get the graph as shown below:
The vector equation of the line through the origin perpendicular to the plane is
.. (x, y, z) = t(2, 3, -1)
so the point of interest will satisfy
.. 2(2t) +3(3t) -(-t) = -3
.. 14t = -3
.. t = -3/14
and its coordinates are (x, y, z) = (-3/7, -9/14, 3/14)