What is the slope of a line perpendicular to the line whose equation is x+2y=8

First, convert the original equation into slope-intercept form:

+2=8
x
+
2
y
=
8
,

2=−+8
2
y
=
−
x
+
8
,

=−/2+4
y
=
−
x
/
2
+
4
,

Since the slope is −1/2
−
1
/
2
, and the product of the slopes of perpendicular lines is −1
−
1
, if the slope of the new line is
m
:

∗−1/2=−1
m
∗
−
1
/
2
=
−
1
,

∗1/2=1
m
∗
1
/
2
=
1
,

=2
m
=
2

Therefore, the slope of the new line is 2. Since the y-intercept of the new line is 0 because it intercepts the origin, the equation of the new line is

=2+0
y
=
2
x
+
0
or

=2
y
=
2
x
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