Question

Write the equation of the line that is parallel to line 3x - 2y = 8 and passes through the point (6, -3). Show ALL steps!

Answer 1

FIRST WRITE THE EQUATION OF 3X-2Y=8 IN THE FORM Y=MX+C TO GET THE REAL GRADIENT OF THE EQUATION

`- 2y = 8 - 3x \\ ( - 2y)/( - 2) = (8)/( - 2) - (3x)/( - 2) \\ y = (3)/(2) x - 4`

PARALLEL LINES HAVE EQUAL GRADIENTS.

AS WE SEE IN THE EQUATION ABOVE THE GRADIENT IS

`(3)/(2)`

IT MEANS THE GRADIENT OF THE NEW EQUATION IS ALSO

`(3)/(2)`

NOW GIVEN THE POINTS WE CAN USE THE KNOWNS TO GET THE VALUE OF C IN THE NEW EQUATION.

`- 3 = (3)/(2) (6) + c \\ - 3 = 9 + c \\ - 3 - 9 = c \\ c = - 12`

`y = (3)/(2) x - 12`