Find the equation of the line that passes through the point (4,-3) and is parallel to the line 2x+3y-6=0?

Answer 1

The slope of a line in standard form Ax + By = C is -A/B

The slope of the given line is -2/3

The slope of a line perpendicular is the opposite reciprocal
which is 3/2 in this case.

A line has a constant slope..
so using the points (x, y) and (4, -3)

[y + 3] / [x - 4] = 3/2

Gives and equation of a line.

If you need this in standard form, cross multiply and simplify

3x - 12 = 2y + 6

3x - 2y = 18

or

3x - 2y - 18 = 0

Answer 2

Find the equation of the line that passes through the
point (4,-3) and is parallel to the line 2x + 3y - 6 = 0.

Parallel lines have the same slope. So if the equations of two lines have the same coefficients for x and y, then they are parallel. Only the constant will be different. So plug the point (4, -3) into the formula for the parallel line.

2(x - 4) + 3(y + 3) = 0
2x - 8 + 3y + 9 = 0
2x + 3y + 1 = 0

Answer 3

the slope of general equation Ax + By + c = 0 is - A/B
comparing 2x + 3y -6 = 0 with Ax + By + c =0the slope of the equation is -2/3 and c =2
the equation of the line through (4 , -3) and slope -2/3 is
[ y - (-3)] = -2/3[x - (4)] +2
y + 3 = -2/3x + 8/3 + 2
2/3x +y = 8/3 +2 - 3
multyply the equation by lcm 3
2x + 3y = 8 + 6 - 9
2x + 3y = 5
2x + 3y - 5 = 0 is the equation of the parallel line

Answer 4

the line 2x + 3y - 6 = 0 should be written in standard form by isolating "y" to show the slope:

3y = -2x + 6
y = (-2/3)x + 2
this shows that the slope is (-2/3)
A line parallel must have the same slope, so you need to find a line that has a slope of (-2/3) and goes through the point (4,-3). You can use point slope form to give the following

y - (-3) = (-2/3)(x-4)

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

Answer 5

you basically ought to organize the 4 opportunities you ought to make y the project of the equation a) y = - 2/3x b) y = 2x - 2 c) y = - 2x - 12 d) y = - 2/3x - 4 then you certainly do exactly the comparable as you're able to do for the different line the place y = mx + b 2x + 3y = 0 may well be rearranged to furnish 3y = - 2x, this ability that: y = - 2/3x conventional form isn't the 2nd you reported yet is, because of the fact the call shows, the conventional one, it is y = mx + b If it must be parallel to y = - 2/3x then its gradient must be -2/3. because of the fact it is going for the period of the factor (-3,-2), and its gradient is two/3, you could artwork out that its y - intercept (the 'b' in y = mx + b) is -4. this means that the equation of the line it is parallel to 2x + 3y = 12 and passes for the period of the factor (-3,-2) is y = -2/3x -4. it particularly is the comparable as d) as quickly as this is been rearranged. the suited answer IS: D) 2x + 3y = -12

Answer 6

3y = - 2x + 6
y = (- 2/3).x + 2
Gradient is (- 2/3) is gradient of parallel line which passes thro` (4,- 3)
Equation of parallel line is:-
y + 3 = (-2/3).(x - 4)
3y + 9 = - 2x + 8
2x + 3y + 1 = 0 is equation of this line.
or
y = (- 2/3).x - 1/3

Answer 7

Since the lines are parallel their slope should be same.
m=-2/3.the formula for the equation of lines is m*(x-xi)=y-yi
so
-2/3*(x-4)=y+3;
y=(-2/3)x-(1/3)

Answer 8

let us take the general linear equation :
y=mx+p
and as this line (d) parallel the other line (d2) then they have the same(m) we fix the equation and we see :
y=( -2x+6)\3.
y= -2\3x+2
then (m)= -2\3
the equation is :
y= -2\3x+p
as long as (4,-3)belongs to d then the equation becomes :
-3= -2\3(4)+p
-3= -8\3+p
P= -9\3+8\3
P=-1\3
and the equation is :
y= -2\3 x -1\3

Answer 9

3y =-2x +6
y =-2/3x +2

slope of the line is -2/3
write point slope form of equation.
y--3= (x-4)(-2/3)
y+3 =-2/3x +8/3