Answer:
What is an equation of the line that passes through the point (-5,8) and is parallel to the line x + y = 8?
Equation of a Line:
There are different ways in solving for the equation of a line depending on the given values. The slope-intercept form can be used when the slope and y-intercept are given. Also, the point-slope form can be used when the slope and a point in the line are given.
Answer and Explanation: 1
Given:
a line that passes through the point
(
−
5
,
8
)
where
x
1
=
−
5
and
y
1
=
8
parallel to the line
x
+
y
=
8
Since parallel lines has the same slope, we solve for the slope of the equation
x
+
y
=
8
by transforming it to its slope-intercept form
y
=
m
x
+
b
where
m
is the slope.
x
+
y
=
8
y
=
−
x
+
8
m
=
−
1
Now, we have a slope
(
m
=
−
1
)
and a point in the line
(
x
1
=
−
5
,
y
1
=
8
)
, we can write an equation of the line using the point-slope form
y
−
y
1
=
m
(
x
−
x
1
)
y
−
y
1
=
m
(
x
−
x
1
)
y
−
8
=
−
1
(
x
−
(
−
5
)
)
y
−
8
=
−
1
(
x
+
5
)
y
−
8
=
−
(
x
+
5
)
Therefore, the equation of the line can be written as
y
−
8
=
−
(
x
+
5
)
