Question

The points (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

The points (7,2) and (-1, 0) lie on a line 4y= x+1. Option B is correct.

Explanation:

• Given data

         Point (A) = (7,2)

         Point (B)= (-1,0)

• In this question, we have to check which pair of satisfied equation of line

• First taking line $\mathbf{7y=3x-7}$ and point A

         $\mathbf{7y=3x-7}$

         Consider L.H.S of above equation

         $\mathbf{L.H.S=7y=7\times 2=14}$

         $\mathbf{R.H.S=3x-7=3\times 7-7=21-7=14}$

        From here it is clear that $\mathbf{L.H.S=R.H.S}$ means point A    

          lie on this line.

         Now check for point B

         $\mathbf{L.H.S=7y=7\times 0=0}$

         $\mathbf{R.H.S=3x-7=3\times (-1)-7=-3-7=-10}$

        From here it is clear that $\mathbf{L.H.S\neq R.H.S}$ ,so point B is    

         not lie on this line.

• Now taking line $\mathbf{4y=x+1}$ and point A

         $\mathbf{4y=x+1}$

         Consider L.H.S of above equation

         $\mathbf{L.H.S=4y=4\times 2=8}$

         $\mathbf{R.H.S=x+1=7+1=8}$

         From here it is clear that $\mathbf{L.H.S=R.H.S}$ means point A    

         lie on this line.

         Now check for point B

         $\mathbf{L.H.S=4y=4\times 0=0}$

         $\mathbf{R.H.S=x+1=-1+1=0}$

          From here it is clear that $\mathbf{L.H.S=R.H.S}$ means point B

          is also lie on this line.

          "So option B is correct".

Answer 2

option B

$4y= x+1$

Explanation:

Given points are (7,2) and (-1,0)

The equation of line passes through the points $(x_1,y_1)$ and $(x_2,y_2)$ is

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

The required equation of the straight line is

$y-2=\frac{0-2}{-1-7} (x-7)$

$\Leftrightarrow (y-2)=\frac{2}{8} (x-7)$

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

$\Leftrightarrow (4y-8)= (x-7)$

$\Leftrightarrow 4y= x-7+8$

$\Leftrightarrow 4y= x+1$