The equation of the line if its slope is −
7
3
and it passes through the point (5,−2) is:
- A3x+7y=29
- B3x−7y=1
- C3x+7y=1
- D3x−7y=29
Solution & Step-by-step Explanation
The point-slope form of the equation of a line is:
y−y
1
=m(x−x
1
)
Given:
Slope (m) = −
7
3
Point (x
1
,y
1
)=(5,−2)
Substituting the values:
y−(−2)=−
7
3
(x−5)
y+2=−
7
3
(x−5)
Multiply both sides by 7:
7(y+2)=−3(x−5)
7y+14=−3x+15
Rearranging the terms to standard form (Ax+By=C):
3x+7y=15−14
3x+7y=1
y−y
1
=m(x−x
1
)
Given:
Slope (m) = −
7
3
Point (x
1
,y
1
)=(5,−2)
Substituting the values:
y−(−2)=−
7
3
(x−5)
y+2=−
7
3
(x−5)
Multiply both sides by 7:
7(y+2)=−3(x−5)
7y+14=−3x+15
Rearranging the terms to standard form (Ax+By=C):
3x+7y=15−14
3x+7y=1