Chapter 1, Problem 1CC

To determine

(a)

The definition of horizontal axis and vertical axis in the coordinate plane.

Answer to Problem 1CC

The horizontal axis is called $x\text{-axis}$ and vertical axis is called $y\text{-axis}$.

Explanation of Solution

In the Cartesian plane or coordinate plane two perpendicular lines intersect each other at origin.

A line that is horizontal with positive direction on right side and negative direction on left side is called as x-axis.

A line that is vertical with positive direction upward and negative direction downward is called as y-axis.

Thus, the horizontal axis is called $x\text{-axis}$ and vertical axis is called $y\text{-axis}$.

To determine

(b)

To find:

The $x$ -coordinate and y -coordinate for the point $\left(2,3\right)$.

Answer to Problem 1CC

The x -coordinate is $2$ and the y -coordinate is $3$ for the point $\left(2,3\right)$.

Explanation of Solution

Given information:

In the coordinate plane the point is $\left(2,3\right)$.

Calculation:

Consider any point $A$ in the coordinate plane and its coordinates be $\left(m,n\right)$.

The first number $m$ is called as $x$ -coordinate of $A$ and the second number $n$ is called as y -coordinate of $A$.

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

Therefore, x -coordinate of the point $\left(2,3\right)$ is 2 and y -coordinate of the point $\left(2,3\right)$ is 3.

To determine

(c)

To explain:

The method to determine whether a given point is on the graph and check that the point $\left(5,3\right)$ is on the graph of the equation $y=2x-1$.

Answer to Problem 1CC

Explanation of Solution

Given information:

The point is $\left(5,3\right)$ and the equation is $y=2x-1$.

Calculation:

Consider any point $A$ in the coordinate plane and its coordinates be $\left(a,b\right)$.

Again consider equation as,

$y=mx+c$ ..... (1)

If the point $\left(a,b\right)$ satisfies the equation (1), then the point $\left(a,b\right)$ lies on the graph of the equation (1).

Now, the given equation is $y=2x-1$ and the given point $\left(5,3\right)$.

Substitute $5$ for $x$ and $3$ for $y$ in equation $y=2x-1$ to check whether the point $\left(5,3\right)$ lies on the graph as,

$\begin{array}{l}3\stackrel{?}{=}2\cdot 5-1\\ 3\stackrel{?}{=}10-1\\ 3\ne 9\end{array}$

Therefore, the point $\left(5,3\right)$ does not satisfy the equation $y=2x-1$.

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