Coordinate System (Parallel/Perpendicular/Intercepts)

**Coordinate System**

The **coordinate system** is a grid system, similar to a map. Its lines are formed by two axes that are drawn perpendicular to each other. The horizontal axis is called the **x-axis,** and the vertical axis is called the **y-axis**. The two intersecting axes form four **quadrants**, numbered I through IV.

The point of intersection (0, 0) is called the **origin**. In an **ordered pair**, the x-coordinate is always listed first and the y-coordinate second.

**Intercept **

**Example 1 **

The *y*intercept is 4

The xintercept is 6

- The graph of 2x + 3y = 12 crosses the x-axis at (6, 0), so its x-intercept is 6.
- The graph of 2x + 3y = 12 crosses the y-axis at (0, 4), so its y-intercept is 4.

**Example 2**

Find the intercepts of the graph

*y* = *x* 5

**Solution**

To find the x-intercept let y = 0 and solve for x

*=*

**y**

*x*5

0 =

*x*5

5 =

*x*

10 = x

*y*=

*5*

**x***y*= (

**0**) 5

*y*= 0 5

*y*= 5

The x-intercept is 10, and the y-intercept is -5.

The graph of the equation contains the points (10, 0) and (0,-5). You could plot these two points and connect them to determine the graph of the line.

**Compare the Slopes of Lines **

Consider two different non-vertical lines 1 and 2. Line 1 has a slope,^{ }m_{1}, and line 2 has a slope, m_{2}. The lines are parallel if and only if they have the same slope; that would make m_{1} = m_{2}.

The lines are perpendicular if their slopes are negative reciprocals of each other. Therefore, perpendicular lines have the following relationships between their slopes:

or