The equation of a line in slope-intercept form is
�
=
�
�
+
�
y=mx+b, where
�
m is the slope and
�
b is the y-intercept.
Since the line we're looking for is parallel to
�
=
−
3
�
+
5
y=−3x+5, it will have the same slope.
Given that the slope of
�
=
−
3
�
+
5
y=−3x+5 is
−
3
−3, the equation of the line parallel to it passing through the point
(
−
6
,
−
8
)
(−6,−8) will be:
−
3
+
y=−3x+b
To find
b, we substitute the coordinates of the point
(
−
6
,
−
8
)
(−6,−8) into the equation:
−
8
=
−
3
(
−
6
)
+
−8=−3(−6)+b
−
8
=
18
+
−8=18+b
=
−
8
−
18
b=−8−18
=
−
26
b=−26
Therefore, the equation of the line is:
=
−
3
−
26
y=−3x−26
