Question

A line whose equation is 3/2y =3x-6 is parallel to a line with a general equation ax+by+c=0 passing through the points (3,2) . Find the value of a,b and c.​

Answer 1

`(1)/(6) x+3y+(13)/(2)` or x + 18y + 39

Explanation:

`(3)/(2) y` =
`3x-6`

→ First multiply everything by 2 to get rid of the fraction

3y = 6x - 12

→ We want to find the equation that's parallel to this line and passes through (3 , 2). The first thing we know about parallel lines is that the gradient is the negative reciprocal so,

`3y = -(1)/(6) x+c`

→ Now we substitute in the values (3 , 2)

`6 =- (1)/(2)+c`

→ Add
`(1)/(2)` to both sides to isolate c

`(13)/(2) =c`

So the equation of the line that is parallel to
`(3)/(2) y` =
`3x-6` is
`3y =- (1)/(6) x+(13)/(2)` but we are not finished we are asked to but the equation in the format

ax + by + c = 0 so,

`3y =- (1)/(6) x+(13)/(2)`

Rearrange

`(1)/(6) x+3y+(13)/(2)`

If the question want's the answer in whole numbers then multiply everything by 6

x + 18y + 39