91Ó°ÊÓ

The x-intercept is the point where the graph of an equation crosses the x-axis. This occurs when the value of y is zero. To find the x-intercept, you can set y to 0 in the equation and solve for x.

Let's take the equation from the exercise: \( x - 2y = -4 \).
By setting \( y = 0 \), the equation becomes:

\[ x - 2(0) = -4 \]
\[ x = -4 \]

This means the x-intercept is at the point \( (-4, 0) \). Plotting this point on the coordinate plane provides one point the line goes through.

The y-intercept is the point where the graph of an equation crosses the y-axis. This happens when the value of x is zero. To find the y-intercept, set x to 0 in the equation and solve for y.

Using the same equation: \( x - 2y = -4 \),
if we set \( x = 0 \), the equation becomes:

\[ 0 - 2y = -4 \]
\[ -2y = -4 \]
\[ y = 2 \]

Thus, the y-intercept is at the point \( (0, 2) \). When we plot this point on the coordinate plane, we identify another key point the line passes through.

A coordinate plane is a two-dimensional surface formed by two perpendicular number lines. These number lines are called axes.

- The horizontal axis is the x-axis.
- The vertical axis is the y-axis.

The point where these axes intersect is called the origin, represented by the coordinates (0, 0).

When graphing linear equations, we plot points using ordered pairs (x, y). For example, the x-intercept \( (-4, 0) \) and the y-intercept \( (0, 2) \). These points are plotted on the coordinate plane, which helps visualize the line represented by the equation.

Linear equations are equations of the first degree in two variables. They can be written in various forms, such as:

- Slope-intercept form: \( y = mx + b \)
- Standard form: \( Ax + By = C \)

The given equation, \( x - 2y = -4 \), is in standard form. To graph a linear equation, you often identify its intercepts:

- The x-intercept: Set y to 0 and solve for x.
- The y-intercept: Set x to 0 and solve for y.

Once you find these intercepts, you can plot them on the coordinate plane and draw a line through these points. This line represents all the solutions to the equation. In this exercise, the line through \( (-4, 0) \) and \( (0, 2) \) would graphically represent the equation \( x - 2y = -4 \).