Just like a line a ray is also infinite in length so it cannot be measured. However, we can measure the distance between any two points on a ray. Before we start discussing ray in detail, let's have a look what line stands for in geometry.

Line: A collection of all points lying along a straight path in a plane is called a line. A line has no endpoints. It extends infinitely in both directions. A line is named by any two points lying on the line. For example, see the picture below:

The above picture is of line $AB$. In mathematical terms, it is written like this: $\overleftrightarrow{AB}$ with arrow heads on both the sides. Note that the line has no endpoints.

The above picture is of line $AB$. In mathematical terms, it is written like this: $\overleftrightarrow{AB}$ with arrow heads on both the sides. Note that the line has no endpoints.

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Note that ray $AB$ and $BA$ are not the same. They are opposite in direction to each other. Symbolically, ray $AB$ would be written as: $\overrightarrow{AB}$ and the ray $BA$ would be written as: $\overrightarrow{BA}$ or $\overleftarrow{AB}$.

For notating a ray, it is imperative to first find out in which direction is the ray going. Say for example a ray looks as follows:

In the above picture, the ray is moving from $H$ towards $G$, so we’ll call it ray $\overrightarrow{HG}$ or $\overleftarrow{GH}$. The other ray would be $\overrightarrow{AB}$.

If there are more than two points on a ray, then each combination could mean a different ray. Say, for example, see the following picture:

In the above picture, we see that rays $BA$ and $BC$ are in opposite direction. Rays $AC$ and $BC$ are in the same direction but yet they do not represent the same ray. Both have a different starting point. So they are different rays. Whereas, in the case of lines, line $AB$, line $BC$ or line $AC$ all three would represent the same line. This is how notations and representations of rays are different from lines.

Like stated earlier, one cannot measure the length of a ray, the, however, angle between two rays can be measured using a protractor. Consider two rays having a common end point. They would look like this:

The above picture has two rays $AB$ and $AC$ in different directions. The angle made by them can be measured using a protractor as shown below:

In the above picture, the two rays $LN$ and $JO$ intersect in the point $P$. That gives us two line segments $LP$ and $JP$ whose lengths can be measured.

Lines $AB$ and $CD$ intersect in point $O$. So now we have four rays: $OA$, $OB$, $OC$, and $OD$. As is evident, $OC$ and $OD$ are opposite rays and so are $OA$ and $OB$.

Rays are commonly used to represent vectors. In the above figure, the ray $V_0$ $V_1$ represents the vector $u$. The ray $V_0\ V_2$ represents the vector $v$. These two rays are coplanar. That means, they lie in the same plane $P$. The ray $V_0\ n$ is perpendicular to the plane $P$. So we say that it is a normal vector to the plane $P$. The ray $P_1\ P_0$ does not line in the plane $P$. It is in a completely different plane with respect to the other rays.

The coordinates of point $B$ are (-2,-2) and those of A are (2,3). So let,

($x_1$,$y_1$) = (-2,-2)

And

($x_2$,$y_2$) = (2,3)

Then the slope of the line BA can be given by the formula:

$m$ = $\frac{y_2\ -\ y_1}{x_2\ -\ x_1}$

Substituting the values into the above formula we have:

$slope$ = $m$ = $\frac{3\ -\ (-2)}{2\ -\ (-2)}$

Simplifying and evaluating that we have:

$m$ = $\frac{3\ +\ 2}{2\ +\ 2}$

$m$ = $\frac{5}{4}$

Using the point-slope formula we have the equation of the line $BA$ as:

$y\ -\ y_1$ = $m(x\ -\ x_1)$

$y\ -\ (-2)$ = $\frac{5}{4}$$(x\ -\ (-\ 2))$

$y\ +\ 2$ = $\frac{5}{4}$ $(x\ +\ 2)$

$y\ +\ 2$ = $\frac{5}{4}$ $x\ +$ $\frac{5}{2}$

$y$ = $(\frac{5}{4})$ $x\ +$ $\frac{5}{2}$$-\ 2$

$y$ = $\frac{5}{4}$ $x\ +$ $\frac{1}{2}$

This is the equation of the line $BA$. Now if we restrict the domain such that the x values cannot be lesser than $-2$, then we get the required equation of the ray $BA$. Thus our final answer would be:

$y$ = $\frac{5}{4}$ $x\ +$ $\frac{1}{2}$,$x\ \geq\ -\ 2$

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