Question

1. Find the slope m and an equation of the tangent line to the graph of the function f a the point (2, 38)

2. Find an equation of the line that passes through the point (9,7) and is perpendicular to the line 5x+3y-4=0

Answer 1

1. "the function" is not specified.
2.
The equation perpendicular to the line
L: 5x+3y-4=0
is
L1 : 3x-5y+k=0
where k is a constant to be determined.

The equation of L1 is obtained by interchanging the coefficients of x and y, <i>and</i> changing the sign of x <i>or</i> y.

The constant k can be determined by the fact that L1 passes through (9,7).
3(9)-5(7)+k=0
k=35-27=8
So
L1: 3x-5y+8=0