Explanation:
the slope of a line is always the factor of x, when the equation is in the form
y = ...
the slope of
y = 2x - 3
is 2.
the slope of
y = -7x - 5
is -7.
for the slope of
16 = 4y - 7x
we need to do some calculation first to bring it into the right format :
4y = 7x + 16
y = 7/4 x + 16/4 = 7/4 x + 4
the slope is
7/4
similar for
0 = -5y + 2x - 5
5y = 2x - 5
y = 2/5 x - 5/5 = 2/5 x - 1
the slope is
2/5
it is important to understand that the slope is always a ratio of y coordinate change / x coordinate change.
so, a slope of e.g 2 is actually the ratio 2/1.
a perpendicular slope switches x and y upside-down, and flips the sign.
e.g. if the original slope is 5 (= 5/1), the perpendicular slope is then -1/5.
the perpendicular slope of
y = 2x - 3
is
-1/2
the perpendicular slope of
y = -7x - 5
is
1/7
the perpendicular slope of
16 = 4y - 7x
is
-4/7
the perpendicular slope of
0 = -5y + 2x - 5
is
-5/2