Question

$x$	$0$	$1$	$2$	$3$	$4$
$y$	$2$	$3$	$4$	$5$	$6$

State whether the given statement is True or False:

The coordinates of points in the table represent the solutions of the equation.

• A. True
• B. False

Answer 1

The correct option is A True

For the points to represent the solution of the equation,

All the points should lie on the same equation.

Finding the equation of the line with 2 points using 2 point form

Point 1 (0,2) and Point 2 (1,3).

Two point form is given by,

$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}{x}_1=0,y_1=2and{x}_2=1,y_2=3\frac{y-2}{3-2}=\frac{x-0}{1-0}\to \frac{y-2}{1}=\frac{x-0}{1}\to x-y+2=0$

Now all the remaining points should satisfy the above equation.

Point (2,4)

$2-4+2=0\to 4-4=0\to LHS=RHS$

Point (3,5)

$3-5+2=0\to -2+2=0\to LHS=RHS$

Point (4,6)

$4-6+2=0\to -2+2=0\to LHS=RHS$

As all the points satisfy the equation,All the points represent the equation.

Answer is True