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

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

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).
 

We’ve answered 318,911 questions. We can answer yours, too.

Ask a question