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}} \\$

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.

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.
$\left( {{x_1} = 7,{y_1} = 2} \right),\left( {{x_2} = - 1,{y_2} = 0} \right)$
$y - 2 = \dfrac{{0 - 2}}{{ - 1 - 7}}\left( {x - 7} \right) \\ y - 2 = \dfrac{{ - 2}}{{ - 8}}\left( {x - 7} \right) \\ y - 2 = \dfrac{1}{4}\left( {x - 7} \right) \\ 4y - 8 = x - 7 \\$