it can be -2x + 3y = 7

find the slope and then find your 'b':

get the given equation into slope intercept form : y=mx + b

-2x + 3y = -4

3y = 2x - 4

y = 2/3x - 4/3

y = mx + b,

m = 2/3, b = -4/3

the slope is m and m is 2/3, so the slope is 2/3.

our line has to be parallel so it needs to have the same slope as the first line, so it also needs a slope of 2/3.

y = mx + b

m = 2/3

y = 2/3(x) + b

our point is (1,3) so plug that in and find b to get the final equation:

3 = 2/3(1) + b

3 = 2/3 + b

3 - 2/3 = b

b = 2 1/3

so in our line with slope of 2/3, our b is 2 1/3,

y = mx + b

m = 2/3

b = 2 1/3

y = 2/3x + 2 1/3

y = 2/3x + 7/3

drghrth45uj45t4534

:-

- 2x + 3y = - 4

3y = 2x - 4

y = (2/3) x - 4/3 ______equation of given line.

Gradient is 2/3

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

y = (2/3) x + 7/3________equation of parallel line

A line parallel to the line whose equation is -2x + 3y = -4

and passes through the point (1, 3):

-2x + 3y = 7

or

2x - 3y = -7

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

-2x+3y=7 or more formally 2x-3y=-7

-2x+3y = -4 ⇒ y = (2/3) x - (4/3)

The equation of the line parallel to -2x+3y = -4 and passing through (1,3) is

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

y = (2/3) x + 2...................ANS

-2(1) + 3(3) = a for some a. Solve for a to find the parallel line through (1, 3).

-2 + 9 = a

a = 7

-2x + 3y = 7

any parallel line

-2x+3y = b

plug in (1,3)

-2(1) + 3(3) = b

-2 + 9 = b

b = -7

-2x + 3y = -7

- 2(1) + 3 ( 3 ) = 7....thus - 2x + 3y = 7