Question

(a) In the coordinate plane, what is the horizontal axis called and what is the vertical axis called?

(b) To graph the ordered pair of numbers $\left(x,y\right)$, you need the coordinate plane. For the point $\left(2,3\right)$, which is the x- coordinate and which is the y-coordinate?

(c) For an equation in the variable x and y, how do you determine whether a given point is on the graph? Is the point$\left(5,3\right)$ on the graph of the equation $y=2x-1$?

Short answer

(a) The horizontal axis is called the x axis and the vertical axis is called the y axis

(b)The x coordinate is 2 and the y coordinate is 3.

(c)The point $\left(5,3\right)$does not exist for the graph of the equation $y=2x-1$.

Step-by-step solution

Part a. Step 1. Define Coordinate Plane.

The plane that consist of a vertical axis and horizontal axis which is used for the graphical representation of equation and inequalities is called a coordinate plane.

Part a. Step 2. Define the horizontal axis.

The horizontal axis is called as the x axis. The horizontal axis goes left and right direction infinitely.

Part a. Step 3. Define the vertical axis.

The vertical axis is called as the y axis. The vertical axis goes up and down direction infinitely.

Thus, the horizontal axis is called the x axis and the vertical axis is called the y axis.

Part b. Step 1. Define Coordinate Plane.

The plane that consist of a vertical axis and horizontal axis which is used for the graphical representation of equation and inequalities is called a coordinate plane.

Part b. Step 2. Define the horizontal axis and vertical axis.

The horizontal axis is called as the x axis. The horizontal axis goes left and right direction infinitely.

The vertical axis is called as the y axis. The vertical axis goes up and down direction infinitely.

Part b. Step 3. Find the x and y coordinate.

The given point is $\left(2,3\right)$.

In the given coordinate, the first point represent the x coordinate and the second point represent the y coordinate.

So, x coordinate is 2 and the y coordinate is 3.

Thus, the x coordinate is 2 and the y coordinate is 3.

Part c. Step 1. Define Coordinate Plane.

The plane that consist of a vertical axis and horizontal axis which is used for the graphical representation of equation and inequalities is called a coordinate plane.

Part c. Step 2. Write the given equation.

The given equation is,

$y=2x-1$

The given point is$\left(5,3\right)$

If the point exist on the graph then it must satisfy the above expression.

Part c. Step 3. Check the point.

Substitute the coordinate value in the given equation.

$$\begin{gathered} 3=2\left(5\right)-1 \\ 3=10-1 \\ 3\ne 9 \end{gathered}$$

The given expression is not equal on the point $\left(5,3\right)$.

Thus, the point$\left(5,3\right)$ does not exist for the graph of the equation $y=2x-1$.