# The blank in the statement “If the point ( 2 , 3 ) is on graph of an equation in x and y, then the equation is satisfied when we replace x by and yby . Also verify whether the point ( 2 , 3 ) lie on the graph of the equation 2 y = x + 1 .”

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.8, Problem 4E
To determine

## To fill: The blank in the statement “If the point (2,3) is on graph of an equation in x and y, then the equation is satisfied when we replace x by       and yby        . Also verify whether the point (2,3) lie on the graph of the equation 2y=x+1 .”

Expert Solution

The complete statement is “If the point (2,3) is on graph of an equation in x and y, then the equation is satisfied when we replace x by 2 and yby3 .The point (2,3)does notlie on the graph of the equation 2y=x+1 .”

### Explanation of Solution

Given information:

The statement “If the point (2,3) is on graph of an equation in x and y, then the equation is satisfied when we replace x by       and yby        . Also verify whether the point (2,3) lie on the graph of the equation 2y=x+1 .”

Consider the provided statement “If the point (2,3) is on graph of an equation in x and y, then the equation is satisfied when we replace x by       and yby        . Also verify whether the point (2,3) lie on the graph of the equation 2y=x+1 .”

The set of all points (x,y) in the Cartesian plane or coordinate plane that satisfy the equation is known as the graph of the equation in x and y coordinates.

Since, the point (2,3) lie on the graph so x will be replaced by 2 and y will be replaced by 3.

As 2 is the x-coordinate and 3 is the y-coordinate.

Substitute the point (2,3) in the equation 2y=x+1 and check whether left hand side is equal to right hand side.

2(3)=2+16=3

The above equality does not hold so, the point (2,3) does not lie on the graph of the equation.

Thus, the complete statement is “If the point (2,3) is on graph of an equation in x and y, then the equation is satisfied when we replace x by 2 and yby3 . The point (2,3)does not lie on the graph of the equation 2y=x+1 .”

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