Question

Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9

Answer 1

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

Explanation:

Let's rewrite the given equation in the form of y= mx +c, where m is the gradient while c is the y-intercept.

2x -3y= 9

3y= 2x -9

Divide by 3 throughout:

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

Thus, the gradient of given line is ⅔.

Parallel lines have the same gradient.

Therefore, gradient of line is ⅔.

Substitute m=⅔ into the equation:

`y = (2)/(3) x + c`

To find the value of c, substitute a pair of coordinates.

When x=4, y= -1,

`- 1= (2)/(3) (4) + c \\ - 1 = (8)/(3) + c \\ c = - 1 - (8)/(3) \\ c = - 3 (2)/(3)`

Substitute the value of c:

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