Question

An equation allows you to find the x- and y-coordinates of any point on the xy-plane.

Answer 1

Answer:

True, An equation allows you to find the x- and y-coordinates of any point on the xy-plane.

Step-by-step explanation:

Given : An equation allows you to find the x- and y-coordinates of any point on the xy-plane.

We have to check whether the given statement is true or not.

Since, An equation in xy- plane is of the form ax + by = c , where a, b and c are real numbers.

Then, we can put different values of x and get values of y  and similarly , by putting different values of y and get values of x.

Thus, we obtain the x- and y-coordinates of any point on the xy-plane.

Example : 2x + 3y = 6

Put x = 0

And solve for y

We have , 3y = 6 ⇒ y = 2

Put y = 0

And solve for x

We have , 2x = 6 ⇒ x = 3

Thus, Points are (0,2) and (3,0)

Thus, An equation allows you to find the x- and y-coordinates of any point on the xy-plane.

 

     

Answer 2

Answer:

The give statement is true.

Step-by-step explanation:

Yes, we can find the coordinates of any point on the xy-plane for any given equation.

For the given equation, we can take random values of x and then find the corresponding y values.

Let us prove this statement with an example.

Let us suppose, we have the equation $y=x^2+4$

For x= 1, we have

$y=1^2+4\\\\y=5$

Thus, the coordinate of the point is (1,4)

Similarly for other values of x, we can find the y values and can find the coordinate.

Thus, we can say that an equation allows us to find the x- and y-coordinates of any point on the xy-plane.