# What is the equation of the line passing through the points (3,2) and (6, 9). Does it pass through the point (9, 12)

justaguide | Certified Educator

The equation of a line passing through the points `(x_1, y_1)` and (x_2, y_2) is `(y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2-x_1)` .

The equation of the line passing through the points (3,2) and (6,9) is:

`(y - 2)/(x - 3) = (9 - 2)/(6 - 3)`

=> `(y - 2)/(x - 3) = 7/3`

=> 3y - 6 = 7x - 21

=> 7x - 3y - 15 = 0

Substituting the coordinates of the point (9, 12) in the equation, 7*9 - 3*12 - 15 = 12. This shows that the line does not pass through the point (9, 12).

The equation of the line passing through (3, 2) and (6, 9) is 7x - 3y - 15 = 0. It does not pass through the point (9, 12)

atyourservice | Student

What is the equation of the line passing through the points (3,2) and (6, 9). Does it pass through the point (9, 12)

`(y-2)/(x-3) = (9 - 2)/(6-3)`

simplify:

`(y-2)/(x-3) = 7 / 3`

cross multiply:

3y - 6 = 7x - 21

move terms to the same side:

3y - 6 - 7x + 21 =0

3y - 7x + 15 =0

plug in  (9, 12) as x and y

3(12) - 7(9) + 15 =0

36 - 63 + 15 = -12

since the number is not 0  the line does not pass through the point (9, 12).