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The coordinate plane is a two-dimensional surface where we can graph equations. It consists of two axes: the horizontal axis, called the x-axis, and the vertical axis, called the y-axis. These axes intersect at a point called the origin, designated as (0, 0). Any point on this plane is identified by a pair of numerical coordinates, written as (x, y). The x-coordinate shows the position along the horizontal axis, while the y-coordinate shows the position along the vertical axis.

When graphing linear equations, such as the one in the exercise, it’s essential to understand how these coordinates align to form a line on the plane. Each linear equation will produce a straight line, and this line can be described using properties such as slope and y-intercept. By plotting points that satisfy the equation and drawing a line through them, you can visually interpret solutions to the equation.

The slope-intercept form of a linear equation is one of the most straightforward formats to understand and graph. It’s written as follows:

### ### y = mx + b

Here, 'y' represents the dependent variable, 'x' the independent variable, 'm' the slope of the line, and 'b' the y-intercept. The slope 'm' describes how steep the line is and the direction it goes (upward or downward).

For instance, let's consider the equation from our exercise: ### ### y = 2x + 4

In this case, 'm' is 2, meaning for each unit 'x' increases, 'y' will increase by 2 units. This positive slope indicates a line rising to the right. In contrast, a negative slope means the line would descend to the right. The slope-intercept form is handy as it quickly tells us both the slope and where the line crosses the y-axis.

The y-intercept is the point where the graph of an equation crosses the y-axis. It occurs when the x-value is zero, showing where the line meets the y-coordinate. In the slope-intercept form, this is denoted by 'b'.

From our example:

### y = 2x + 4In this equation, 'b' is 4, which tells us the line crosses the y-axis at (0, 4). This means that no matter the slope, the line will always intersect the y-axis at this value. 

Knowing the y-intercept is crucial for graphing the equation because it's one of the key points needed to draw the line. Once you have the y-intercept, you can use the slope to find other points on the line, making it easier to graph the equation accurately.

• Start at the y-intercept (0,4).
• From there, use the slope to find additional points. In this case, for every 1 unit you move to the right, move 2 units up because the slope is 2.