The line passing through (2,−1) and (y,−2) is parallel to the line passing through (−3,4) and (0,3). Find y.
- A-2
- B2
- C5
- D-5
Solution & Step-by-step Explanation
Since the two lines are parallel, their slopes must be equal (m
1
=m
2
).
The formula for the slope of a line passing through (x
1
,y
1
) and (x
2
,y
2
) is:
m=
x
2
−x
1
y
2
−y
1
Slope of the first line (m
1
) passing through (2,−1) and (y,−2):
m
1
=
y−2
−2−(−1)
=
y−2
−1
Slope of the second line (m
2
) passing through (−3,4) and (0,3):
m
2
=
0−(−3)
3−4
=
3
−1
Equating the slopes:
y−2
−1
=
3
−1
y−2=3
y=5
1
=m
2
).
The formula for the slope of a line passing through (x
1
,y
1
) and (x
2
,y
2
) is:
m=
x
2
−x
1
y
2
−y
1
Slope of the first line (m
1
) passing through (2,−1) and (y,−2):
m
1
=
y−2
−2−(−1)
=
y−2
−1
Slope of the second line (m
2
) passing through (−3,4) and (0,3):
m
2
=
0−(−3)
3−4
=
3
−1
Equating the slopes:
y−2
−1
=
3
−1
y−2=3
y=5