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

Answer: (B)

$4y=x+1$

If a point lies on a line, it satisfies the equation of that line.
Here, we will check points $(7,2)$ and $(-1,0)$ satisfies which equation given in options.
Let's take option $A$, $7y=3x-7$
For point $(7,2)$, LHS $=7\left(2\right)=14,$ RHS $=3\left(7\right)-7=14$
i.e, LHS $=$ RHS.

Hence, $(7,2)$ lies on the line $7y=3x-7$
For point $(-1,0)$, LHS $=7\left(0\right)=0,$ RHS $=3(-1)-7=-10$
i.e.LHS $\ne$ RHS. Hence $(-1,0)$ does not lie on the line $7y=3x-7$.
Option $B$, $4y=x+1$
For point $(7,2)$, LHS $=4\left(2\right)=8,$ RHS $=7+1=8$
i.e, LHS $=$ RHS.

Hence $(7,2)$ lies on the line $4y=x+1$
For point $(-1,0)$, LHS $=4\left(0\right)=0,$ RHS $=-1+1=0$
i.e, LHS $=$ RHS. Hence $(-1,0)$ lies on the line $4y=x+1$
Hence, $(7,2)$ and $(-1,0)$ lie on the line $4y=x+1$
Option $C$, $y=7x+7$
For point $(7,2)$, LHS $=2,$ RHS $=7\left(7\right)+1=50$
i.e, LHS $\ne$ RHS. Hence $(7,2)$ does not lie on the line $y=7x+7$
For point $(-1,0)$, LHS $=0$, RHS $=7(-1)+7=0$
i.e. LHS $=$ RHS. Hence $(-1,0)$ lies on the line $y=7x+7$
Option $D$, $x=4y+1$
For point $(7,2)$, LHS $=7$, RHS $=4\left(2\right)+1=9$
i.e. LHS $\ne$ RHS. Hence $(7,2)$ does not lie on the line $x=4y+1$
For point $(-1,0)$, LHS $=-1$, RHS $=0+1=1$
i.e. LHS $\ne$ RHS. Hence $(-1,0)$ lies on the line $x=4y+1$