Question

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

Answer 1

Answer:

$y = \frac{2}{3} x - 3 \frac{2}{3}$

Step-by-step 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:

$y = \frac{2}{3} x - 3$

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:

$y = \frac{2}{3} x + c$

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

When x=4, y= -1,

$- 1= \frac{2}{3} (4) + c \\ - 1 = \frac{8}{3} + c \\ c = - 1 - \frac{8}{3} \\ c = - 3 \frac{2}{3}$

Substitute the value of c:

$y = \frac{2}{ 3} x - 3 \frac{2}{3}$