Question

$x$	$-1$	$0$	$1$	$2$
$y$	$-3$	$-1$	$1$	$3$

Which equation fits the data in the table ?

• A. $y=x-2$
• B. $y=2x-1$
• C. $y=3x-3$
• D. $y=x+1$

Answer 1

Answer: (B)

$y=2x-1$

The equation which is satisfied with all the data points is the correct answer.
Option $A,y=x-2$
At $x=-1,y=-3$, LHS $=-3$, RHS $=-1-2=-3$
LHS $=$ RHS
Hence, $(-1,-3)$ lies on the line $y=x-2$
At $x=0,y=-1$, LHS $=-1$, RHS $=0-2=-2$
LHS $\ne$ RHS
Hence, $(0,-1)$ does not lie on the line $y=x-2$
Hence, option $A$ is incorrect.
Option $B$, $y=2x-1$
At $x=-1,y=-3$, LHS $=-3$, RHS $=2(-1)-1=-3$
LHS $=$ RHS
Hence, $(-1,-3)$ lies on the line $y=2x-1$
At $x=0,y=-1$, LHS $=-1$, RHS $=0-1=-1$
LHS $=$ RHS
Hence, $(0,-1)$ lie on the line $y=2x-1$
At $x=1,y=1$, LHS $=1$, RHS $=2\left(1\right)-1=1$
LHS $=$ RHS
Hence, $(1,1)$ lie on the line $y=2x-1$
At $x=2,y=3$, LHS $=3$, RHS $=2\left(2\right)-1=3$
LHS $=$ RHS
Hence, $(2,3)$ lie on the line $y=2x-1$
Hence, $y=2x-1$ fits to given data.
We can similarly check for other options also.