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The x-intercept of a line is the location where the line crosses the x-axis of the coordinate plane. At this point, the value of the y-coordinate is zero because the line is right on the x-axis. This is a crucial intersection because it gives insight into where a line touches or crosses this horizontal axis.
To find the x-intercept from an equation, you simply set \( y = 0 \) and solve for \( x \). For the equation \( y = -2x - 4 \), we substitute \( 0 \) for \( y \) and solve as follows:

• Starting with \( 0 = -2x - 4 \)
• We add 4 to both sides to get \( 4 = -2x \)
• Then divide both sides by -2 to find \( x = -2 \)

Thus, the x-intercept is \((-2, 0)\). Remember, the x-intercept isn't just a number; it's a point on the coordinate plane.

The y-intercept is the spot where the line crosses the y-axis. Here, the x-coordinate is zero because it lies directly on the y-axis itself.
Finding the y-intercept is quite straightforward, especially with the equation in slope-intercept form \( y = mx + b \), where \( b \) directly represents the y-intercept. In our equation \( y = -2x - 4 \), \( b = -4 \).

• Set \( x = 0 \) in the equation: \( y = -2(0) - 4 \)
• This simplifies to \( y = -4 \)

Therefore, the line crosses the y-axis at the point \((0, -4)\). The y-intercept is essential in sketching the graph as it provides one of the pivotal points that determine the line's position.

The coordinate plane is like a map that helps us locate points using two numbers known as coordinates, usually written as \( (x, y) \). This plane consists of two perpendicular axes:

• The horizontal axis, called the x-axis
• The vertical axis, known as the y-axis

On this plane, every point is an intersection of a parallel from the x-axis and a parallel from the y-axis. For example, the point (3, -2) tells us to go right 3 units along the x-axis and downward 2 units along the y-axis.
To graph a linear equation, you need to plot points on this plane. The intercepts, such as the x-intercept \((-2, 0)\) and y-intercept \((0, -4)\), are vital in this process. Plot these points and draw a straight line passing through them. This forms the graph of the equation, illustrating how x and y relate to one another within the equation.