Answer: The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is:
y
=
m
x
+
b
y
=
−
3
2
x
−
1
Where
m
is the slope and
b
is the y-intercept value.
Therefore the slope of this line is:
m
=
−
3
2
Parallel lines by definition have the same slope. Therefore, we can substitute this slope into the formula giving:
y
=
−
3
2
x
+
b
We have been given a point on the parallel line so we can substitute the values of the point for
x
and
y
and solve for
b
y
=
−
3
2
x
+
b
becomes:
−
1
=
(
−
3
2
×
−
2
)
+
b
−
1
=
3
+
b
−
3
−
1
=
−
3
+
3
+
b
−
4
=
0
+
b
−
4
=
b
We can now substitute the slope and y-intercept into the formula giving:
y
=
−
3
2
x
+
−
4
y
=
−
3
2
x
−
4
Explanation: