91Ó°ÊÓ

A coordinate plane is a two-dimensional plane formed by the intersection of two perpendicular lines called the x-axis (horizontal) and the y-axis (vertical).
This plane is divided into four quadrants which are:

• Quadrant I (both x and y are positive)
• Quadrant II (x is negative, y is positive)
• Quadrant III (both x and y are negative)
• Quadrant IV (x is positive, y is negative)

Each point on the plane is defined by an ordered pair \((x, y)\), where 'x' represents the position on the x-axis and 'y' represents the position on the y-axis. For example, the point \((3, -2)\) is located 3 units to the right of the origin (0,0) on the x-axis and 2 units down on the y-axis.
The origin is the point where the x-axis and y-axis intersect, represented by the ordered pair \((0,0)\).

A linear equation is an equation that makes a straight line when it is graphed. The standard form of a linear equation in two variables is \[Ax + By = C\], where 'A', 'B', and 'C' are constants. The simplest form of a linear equation is often written as \[y = mx + b\], where 'm' is the slope (the rate of change) and 'b' is the y-intercept (the value of y when x is 0).
In this exercise, the linear equation we deal with is \[y = x + 2\]. This particular equation means that for any given x-value, you can find the corresponding y-value by simply adding 2 to the x-value.
For instance, if x = 1, then y = 1 + 2 = 3. The slope 'm' in this equation is 1 (since the coefficient of x is 1), and the y-intercept 'b' is 2. The slope of 1 means that for every 1 unit increase in x, y increases by 1 unit.

Graphing points is the process of marking specific coordinates on a coordinate plane. Each point is defined by an ordered pair \((x, y)\). To graph a point, follow these steps:

• Identify the x-value and locate its position on the x-axis.
• Identify the y-value and locate its position on the y-axis.
• Find where these two values intersect on the graph and mark the spot.

In the given exercise, we calculated the points to be \((-3, -1)\), \((0, 2)\), and \((4, 6)\). Plotting these points involves:

Moving 3 units to the left on the x-axis and 1 unit down on the y-axis for \((-3, -1)\).

Staying at the origin and moving 2 units up for \((0, 2)\).

Moving 4 units to the right and 6 units up for \((4, 6)\).

Once all points are plotted, you can draw a line through them to see the graph of the linear equation \[y = x + 2\].