Question 723775: On your responses please include the text of the question, your set-up and work, and answer using full sentences.
5. Determine the equations of:
(a) the line that passes through the point ( -5, 3) and that is parallel to the line with equation y = 2x -3
(b) the line that passes through the point (2, 4) that is perpendicular to the line with equation y = (1/2)x -1
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 1 y = 2 x -3
Divide by 1
y = 2 x -3
Compare this equation with y=mx+b
slope m = 2
The slope of a line parallel to the above line will be the same
The slope of the required line will be 2
m= 2 ,point ( -5 , 3 )
Find b by plugging the values of m & the point in
y=mx+b
3 = -10 + b
b= 13
m= 2
Plug value of the slope and b in y = mx +b
The required equation is y = 2 x + 13
1 y = 1/ 2 x -1
Divide by 1
y = 1/ 2 x + -1
Compare this equation with y=mx+b, m= slope & b= y intercept
slope m = 1/2
The slope of a line perpendicular to the above line will be the negative reciprocal -2
Because m1*m2 =-1
The slope of the required line will be -2
m= -2 ,point ( 2 , 4 )
Find b by plugging the values of m & the point in
y=mx+b
4 = -4 + b
b= 8
m= -2
The required equation is y = -2 x + 8
.
m.ananth@hotmail.ca
|
|
|
