Find the equation of the lines that are both passing through the point (-5,6) with slopes 2/3 and -4.
Answers
Answer:
- 3y - 2x - 28 = 0
- x + 4y - 19 = 0
Step-by-step explanation:
We are given the slopes of two points and given the statement that these both lines passes through a common point.
To find the equations of such straight line whose slope and one point are given, we use the slope point form of straight lines which is given by,
- y - y1 = ( x - x1 ) m
Here,
- x1 and y1 are the points through which the line passes.
- m is the slope of line
For first line,
Equation is given by :
=> y - y1 = ( x - x1 ) m
Substitute the known values
=> y - 6 = ( x - (-5) ) 2/3
=> y - 6 = (x + 5)2/3
=> (y - 6)3 = (x + 5)2
=> 3y - 18 = 2x + 10
=> 3y - 2x - 18 - 10 = 0
=> 3y - 2x - 28 = 0
This is the required equation of first line.
For second line,
Equation is given by :
=> y - y1 = ( x - x1 ) m
=> y - 6 = ( x - ( -5) ) ( -4)
=> y - 6 = ( x + 5 ) ( -4)
=> (y - 6)(-4) = x + 5
=> -4y + 24 = x + 5
=> 0 = x + 5 + 4y - 24
=> 0 = x + 4y - 19
This is the required equation of second line.