Question

Points A(x, y), B(3, −2) and C(4, −5) are collinear. The value of y in terms of x is ______.

पर्याय

• 3x − 11

• 11 − 3x

• 3x − 7

• 7 − 3x

Answer 1

Points A(x, y), B(3, −2) and C(4, −5) are collinear. The value of y in terms of x is 7 − 3x.

Explanation:

For points to be collinear, the slope between any two pairs must be the same.

So, let’s find the slope using B(3, –2) and C(4, –5):

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (-5 - (-2))/(4 - 3)`

`m = (-3)/1`

∴ m = –3

Now, using A(x, y) and B(3, −2):

`m = (y_2 - y_1)/(x_2 - x_1)`

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

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

y + 2 = −3(x − 3)

y + 2 = −3x + 9

y = −3x + 9 − 2

y = −3x + 7

∴ y = 7 − 3x