Question & Answer
QUESTION

The points ( 7, 2 ) and ( -1, 0 ) lie on a line $ \ldots \ldots $
$
  {\text{A}}{\text{. 7y = 3x - 7}} \\
  {\text{B}}{\text{. 4y = x + 1}} \\
  {\text{C}}{\text{. y = 7x + 7}} \\
  {\text{D}}{\text{. x = 4y + 1}} \\
$

ANSWER Verified Verified
Hint: -To solve this question we have two points given and we know two point form of line so we will write an equation of line using these two given points. And then just check which option is matching.

Complete step by step answer:
We have
( 7, 2 ), ( -1 ,0 )
Two point form of a line if two points are $\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right)$ is
$y - {y_1} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\left( {x - {x_1}} \right)$ using this formula or form of line we will write equation of line.
Here in this question,
$\left( {{x_1} = 7,{y_1} = 2} \right),\left( {{x_2} = - 1,{y_2} = 0} \right)$
$
  y - 2 = \dfrac{{0 - 2}}{{ - 1 - 7}}\left( {x - 7} \right) \\
  y - 2 = \dfrac{{ - 2}}{{ - 8}}\left( {x - 7} \right) \\
  y - 2 = \dfrac{1}{4}\left( {x - 7} \right) \\
  4y - 8 = x - 7 \\
$
On rearranging we get,
4y = x +1
Hence option B is the correct option.

Note: -Whenever we get this type of question the key concept of solving is we can write an equation of line using two points. And here one thing is important. If this type question comes in an exam you have no need of writing an equation just put the points in option and check which option is satisfying that will be answered.