what is the equation of the line perpendicular to 2x+5y=20 and containing the point (10,4)Please explain with steps

Given the point (10, 4) is on the equation of the
line.

Then, we know that the equation of the line
is:

y-y1= m(x-x1)

We will
substitute with the point (10, 4)

==> y- 4= m
(x-10)

Now we need to find the slope
m.

We are given that the perpendicular line is 2x+5y=
20

Then we will find the
slope.

==> 5y= -2x +
20

==> y= -2/5 x +
4

Then the slope of the perpendicular line is
-2/5

But we know that the product of the slopes of two
perpendicular line is -1.

==> -2/5 * m =
-1

==> m= 5/2

Now we
will substitute into the equation of the line.

==>
y-4= (5/2) (x-10)

==> y-4 = (5/2)x -
25

==> y= (5/2)x - 25 +
4

==> y= (5/2)x -
21

Multiply by 2.

==>
2y= 5x - 42

==> 2y - 5x + 42 = 0 is
the equation of the line.