Question

which of the following points does not lie on the line Y=3x+4? (a) (2,10) , (b) (4,12) (c) (1,7) (d) (-1,1)​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

PROCESS

A general equation of any line is

$ax + by + c = 0$

Now a point

$(x_1, y_1)$

lies on the above straight line if the point satisfies the equation

$ax + by + c = 0$

Which means if

$ax_1 + by_1 + c = 0$

EVALUATION

The given equation of the line is

$y = 3x + 4 \: \: \: \: ........(1)$

1. CHECKING FOR THE POINT ( 2, 10 )

Putting x = 2 & y = 10 in both sides of Equation (1) we get

$10 = \: (3 \times 2) + 4$

$\implies \: 10 = 10$

Which is true

Hence (2,10) is a point on the line

2. CHECKING FOR THE POINT ( 4, 12 )

)Putting x = 4 & y = 12 in both sides of Equation (1) we get

$12 = (3 \times 4) + 4$

$\implies \: 12 = 6$

Which is false

Hence ( 4 ,12 ) is a point not a on the line

3. CHECKING FOR THE POINT ( 1, 7 )

)Putting x = 1 & y = 7 in both sides of Equation (1) we get

$7 = (3 \times 1) + 4$

$\implies \: 7 = 7$

Which is true

Hence ( 1 ,7 ) is a point on the line

4. CHECKING FOR THE POINT ( - 1 , 1 )

)Putting x = - 1& y = 1 in both sides of Equation (1) we get

$1 = \{3 \times (- 1) \} + 4$

$\implies \: \: 1 = 1$

Which is true

Hence ( - 1, 1 ) is a point on the line

$\red{ \fbox{HENCE ( 4, 12) is the only point </strong><strong>does</strong><strong> </strong><strong>not on the line }}$