Find Equation of the Line?

Question

Find an equation of the line having the given properties. Express your answers using the general form of the equation of a line and also the slope-intercept form of the equation of a line.

(1) Parallel to the line x + y = 2; having the point (1, -3)

(2) Perpendicular to the line 3x - y = - 4;
having the point (-2, 4)

Answer 1

(1) Parallel to the line x + y = 2; having the point (1, -3)

finding the slope of the given line
x + y = 2
y = 2-x
slope of the given line is -1

sloe of parallel lines are equal
so slope of the required line is also -1

we have a point & the slope, so to fond the equation of the line, the formula is

(y-y1)=m(x-x1)
m=-1, (x1,y1)=(1,-3)
(y-{-3})=-1(x-1)
(y+3)=-1(x-1)
y+3=-x+1
y=-x+1-3
y=-x-2


so the equation of the line is y=-x-2


(2) Perpendicular to the line 3x - y = - 4;
having the point (-2, 4)

finding the slope of the given line
3x - y = - 4
- y = - 4-3x
y = 4+3x

so the slope of the given line is 3
the product of 2 perpendicular lines is -1.
so the slope of the required line is
m1*m2=-1
3*m2=-1
m2=-1/3

so the slope of the equired line is =-1/3

we have a point & the slope, so to fond the equation of the line, the formula is

(y-y1)=m(x-x1)
m=-1/3, (x1,y1)=(-2,4)
(y-{4})=-1/3(x-{-2})
(y-4)=-1/3(x+2)
3* (y-4)=-1(x+2)
3y-12=-x-2
3y=-x-2+12
3y=-x+10

so the equation of the line is3y=-x+10

Answer 2

Question 1
y = - x + 2 has m = - 1
Equation of parallel line is:-
y + 3 = (-1) (x - 1)
y + 3 = - x + 1
y = - x - 2

Question 2
y = 3x + 4 has m1 = 3
Perpendicular line has m2 = - 1/3
Equation of perpendicular line is:-
y - 4 = (-1/3) (x + 2)
y = (-1/3) x - 2/3 + 4
y = (-1/3)x + 10/3

Answer 3

(1) Any line parallel to the line x+y=2 is x+y = c ............. (eqn 1)

As this line passes through (1,-3), this point must satisfy the eqn.
ie 1 + (-3) = c
=> c = -2. Substitute this value of c in eqn (1) we get the answer-
x + y + 2 = 0 ........ Answer

..........................................................................................

Q2 Perpendicular to the line 3x - y = - 4; having the point (-2, 4)

Soln : Any line perp. to the given line is
x + 3y = c . Where c is a constant. As this line has the point ( -2, 4) lying on it.
- 2 + 3 (4 ) = c => c = 10

Hence the required line is -
x + 3y = 10.......... Answer

Answer 4

1) y=-x-2
2) y=(-1/3)x+(10/3)

Answer 5

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Answer 6

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