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Question 515136: Give an equation to a line that satisfy the following:
1.) Passes through (0, 6) and is parallel to y = 4x - 6
2.) Passes through (-2, 3) and is perpendicular to 3x - 2y = 8
3.) has the same x intercept as y = -2x + 4 and the same y intercept as
7x - 4y = -3
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 1 y = 4 x -6
Divide by 1
y = 4 x -6
Compare this equation with y=mx+b
slope m = 4 0.8
m= 4 ,point ( 0 , 6 )
Find b by plugging the values of m & the point in
y=mx+b
6 = 0.00 + b
b= 6
m= 4
Plug value of the slope and b in y = mx +b
The required equation is
y = 4 x + 6
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3 x -2 y = 8
Find the slope of this line
-2 y = -3 x + 8
Divide by -2
y = 3/2 x -4
Compare this equation with y=mx+b
slope m = 3/2
The slope of a line perpendicular to the above line will be the negative reciprocal
m1*m2=-1
The slope of the required line will be -2/3
m= - 2/3 ,point ( -2 , 3 )
Find b by plugging the values of m & the point in
y=mx+b
3 = 1.33 + b
b= 1.67
m= - 2/3
The required equation is y =- 2/ 3x+5/ 3
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has the same x intercept as y = -2x + 4 and the same y intercept as
7x - 4y = -3
y = -2x + 4
for x intercept plug y=0
x intercept = 2
(2,0) is the intersection point
7x - 4y = -3
For y intercept plug x=0
-4y=-3
y=3/4
(0,3/4) is the y intercept point
The line passes through (2,0) & (0,3/4)
x1 y1 x2 y2
2 0 0 0.75
slope m = (y2-y1)/(x2-x1)
( 0.75 - 0 )/( 0 - 2 )
( 0.75 / -2 )
m= - 3/ 8
Plug value of the slope and point ( 2 , 0 ) in
Y = m x + b
0.00 = - 3/4 + b
b= 0 - - 3/4
b= 3/ 4
So the equation will be
Y = - 3/8 x + 3/4
m.ananth@hotmail.ca
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