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Understanding how to use the coordinate plane is essential when graphing linear equations. The coordinate plane is a two-dimensional system where every point is defined by a pair of numbers:

• The x-coordinate (horizontal position)
• The y-coordinate (vertical position)

These are also called Cartesian coordinates and are generally provided in the form (x, y).
When graphing, the horizontal axis is known as the x-axis, and the vertical axis is the y-axis. The point where they intersect is called the origin, which has the coordinates (0,0). This setup allows us to visually represent mathematical relationships such as linear equations.
In this case, graphing the equation involves marking various points by using calculated x and y coordinates on this plane and then connecting those points to display the behavior of the function.

The slope-intercept form is a way to express linear equations. It is written as:
\[ y = mx + b \]
Here, 'm' represents the slope of the line, which indicates steepness and direction. Meanwhile, 'b' is the y-intercept, which is the point where the line crosses the y-axis.

• The slope 'm' is calculated as the ratio of the change in y to the change in x (rise over run).
• The y-intercept 'b' tells us the value of y when x equals zero.

For the equation \( y = 2x - 4 \), the slope \( m = 2 \) demonstrates that for every additional unit to the right (positive x-direction), the line goes up by 2 units. The y-intercept \( b = -4 \) indicates that the line crosses the y-axis at -4. Understanding this setup helps us in plotting and predicting other points on the line.

Plotting points is a technique used to visually map equations on the coordinate plane. It allows us to see the geometric nature of equations. After calculating the x and y values from the equation, we plot them as individual points.

• Start by identifying the x-coordinate value and move along the x-axis.
• Then, find the corresponding y-coordinate and move up or down along the y-axis.

Once a point is plotted at the intersection of these coordinates, proceed to the next point. In our exercise, points like (-3, -10), (-2, -8), and so on, are plotted sequentially.
Connecting these plotted points should form a straight line, reflecting the nature of linear equations. This visual representation can give a better understanding of how x values affect y and makes it easier to foresee where new points might lie. Therefore, plotting is a crucial step in visualizing mathematical relationships between variables.