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Question 570882: I need help with 6 problems, I have been trying to figure them out for 2 days now and have not been able too. Please help, here are the questions.
Find an equation of the line containing the given pair of points.
(1/4, -1/2) and (3/4, 6)
What is the equation of the line? y=
second question
Find an equation of the line having the given slope and containing the given point.
m=6/7, (1, -7)
The equation of the line is Y=
Third question
Find an equation of the line containing the given pair of points.
(-1, -2) and (-4, -6)
The equation of the line in slope-intercept from is y=
Fourth Question
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b
(-4, 7); 4x=3y+2
The equation of the line is y=
Fifth question
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b
(5, 7); 5x+y=4
the equation of the line is y=
Sixth question
Write an equation of the line containing the given point and perpendicular to the given line.
(5, -4); 4x+3y=8
The equation of the line is y=
I have no clue how to solve these problems, any help is greatly appreciated.
Thanks again
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Find an equation of the line containing the given pair of points.
(1/4, -1/2) and (3/4, 6)
x1 y1 x2 y2
1/ 4 1/ 2 3/ 4 6
slope m = (y2-y1)/(x2-x1)
( 6 - 1/2 )/( 3/4 - 1/4 )
( 5.5 / 0.5 )
m= 11
Plug value of the slope and point ( 1/4 , 1/2 ) in
Y = m x + b
1/2 = 11/4 + b
b= 0.5 - 11/4
b= -9/ 4
So the equation will be
Y = 11 x -9/4
What is the equation of the line? y=
second question
Find an equation of the line having the given slope and containing the given point.
m=6/7, (1, -7)
m= 6/ 7
Plug value of the slope and point ( 1, -7
Y = m x + b
-7.00 = 6/7 + b
b= -7 - 6/7
b= -55/ 7
So the equation will be
Y = 6/7 x -55/7
The equation of the line is Y=
Third question
Find an equation of the line containing the given pair of points.
(-1, -2) and (-4, -6)
x1 y1 x2 y2
-1 -2 -4 -6
slope m = (y2-y1)/(x2-x1)
( -6 - -2 )/( -4 - -1
( -4 / -3 )
m= 4/ 3
Plug value of the slope and point ( -1 , -2 ) in
Y = m x + b
-2.00 = -4/3 + b
b= -2 - -4/3
b= - 2/ 3
So the equation will be
Y = 4/3 x - 2/3
The equation of the line in slope-intercept from is y=
Fourth Question
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b
(-4, 7); 4x=3y+2
4 x + -3 y = 2
Find the slope of this line
make y the subject
-3 y = -4 x + 2
Divide by -3
y = 4/ 3 x - 2/3
Compare this equation with y=mx+b
slope m = 4/3
The slope of a line parallel to the above line will be the same
The slope of the required line will be 4/3
m= 4/3 ,point ( -4 , 7 )
Find b by plugging the values of m & the point in
y=mx+b
7 = -16/3 + b
b= 37/3
m= 4/3
Plug value of the slope and b in y = mx +b
The required equation is y = 4/3 x + 37/3
The equation of the line is y=
Fifth question
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b
(5, 7); 5x+y=4
5 x + 1 y = 4x+5y=2
Find the slope of this line
make y the subject
1 y = -5 x + 4
Divide by 1
y = -5 x + 4
Compare this equation with y=mx+b
slope m = -5
The slope of a line parallel to the above line will be the same
The slope of the required line will be -5
m= -5 ,point ( 5 , 7 )
Find b by plugging the values of m & the point in
y=mx+b
7 = -25.00 + b
b= 32
m= -5
Plug value of the slope and b in y = mx +b
The required equation is y = -5 x + 32
the equation of the line is y=
Sixth question
Write an equation of the line containing the given point and perpendicular to the given line.
(5, -4); 4x+3y=8
4 x + 3 y = 8
Find the slope of this line
3 y = -4 x + 8
Divide by 3
y = -1 1/ 3 x + 2.67
Compare this equation with y=mx+b
slope m = -4/ 3
The slope of a line perpendicular to the above line will be the negative reciprocal 3/4
m1*m2=-1
m= 3/4 ,point ( 5 , -4 )
Find b by plugging the values of m & the point in
y=mx+b
-4 = 15/4 + b
b= -31/4
m= 3/4
The required equation is y = 3/ 4 x -31/ 4
The equation of the line is y=
m.ananth@hotmail.ca
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