The line passing through (−2,5) and (6,b) is perpendicular to the line 20x+5y=3. Find b?
- A-7
- B4
- C7
- D-4
Solution & Step-by-step Explanation
First, let us find the slope (m
1
) of the given line 20x+5y=3:
5y=−20x+3⟹y=−4x+
5
3
So, the slope m
1
=−4.
Since the line passing through (−2,5) and (6,b) is perpendicular to this line, the product of their slopes must be −1:
m
1
×m
2
=−1⟹−4×m
2
=−1⟹m
2
=
4
1
Now, find the slope m
2
using the two points (−2,5) and (6,b):
m
2
=
6−(−2)
b−5
=
8
b−5
Equating the two expressions for m
2
:
8
b−5
=
4
1
b−5=
4
8
b−5=2
b=7
1
) of the given line 20x+5y=3:
5y=−20x+3⟹y=−4x+
5
3
So, the slope m
1
=−4.
Since the line passing through (−2,5) and (6,b) is perpendicular to this line, the product of their slopes must be −1:
m
1
×m
2
=−1⟹−4×m
2
=−1⟹m
2
=
4
1
Now, find the slope m
2
using the two points (−2,5) and (6,b):
m
2
=
6−(−2)
b−5
=
8
b−5
Equating the two expressions for m
2
:
8
b−5
=
4
1
b−5=
4
8
b−5=2
b=7