Question

The point (7,2) and (-1,0) lie on a line:
a) 7y= 3x -7
b) 4y= x+ 1
c) y= 7x + 7
d) x= 4y + 1​

Answer 1

Answer :

Option b) 4y = x + 1

Explanation :

If a point lie on a line then it must satisfies the equation.

So, let we put the points one by one and check whether LHS is equal to RHS or not.

a) 7y = 3x - 7

For point (7,2)

LHS : 7 ( 2 ) = 14

RHS : 3 ( 7 ) - 7 = 14

LHS = RHS

For point ( -1, 0 )

LHS : 7 (0) = 0

RHS : 3 ( -1) - 7 = -10

LHS ≠ RHS

•°• These points don't lie on line 7y = 3x - 7

b) 4y = x + 1

For point (7,2)

LHS : 4 ( 2 ) = 8

RHS : 7 + 1 = 8

LHS = RHS

For point (-1,0)

LHS : 4 ( 0 ) = 0

RHS : -1 + 1 = 0

LHS = RHS

•°• These points lie on the line 4y = x + 1

Hence, option B) is correct.

Answer 2

$\huge\bold\green{Question}$

The point (7,2) and (-1,0) lie on a line ?

a) 7y= 3x -7

b) 4y= x+ 1

c) y= 7x + 7

d) x= 4y + 1

$\huge\bold\blue{Solution}$

Option (a) 4y = x + 1 is correct answer

The points (7, 2) and (− 1 , 0 ) lie on a line

Firstly we have to find slope of the line ,

formula for finding slope is

$\large \huge \sf \green{m = \frac{ y_{2} - y_{1} }{x_{2} - x_{1}} }$

By substituting the values , we get slope (m) :

$\sf {m = \frac{ 0 - 2 }{ - 1 - 7} }$

$\sf {m = \frac{ - 2 }{ - 8} = \frac{1}{4} }$

$\tt \large \blue{slope(m) = \frac{1}{4} }$

Point slope form of line is →

$\large \huge \sf \green{ { y_ - y_{1} = m({x - x_1 )}}}$

$\implies \sf{y - 2 = \frac{1}{4} (x - 7)}$

$\implies \sf{4y - 8 = x - 7}$

$\implies \sf \red{4y = x + 1}$

Hence, option (a) 4y = x + 1 is correct option