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The x-intercept is a pivotal concept when dealing with linear functions. It is where the graph of the function crosses the x-axis. This means that at the x-intercept, the value of the function, often written as \( F(x) \), is zero.

To find the x-intercept, you need to solve for \( x \) when \( F(x) = 0 \). For a function like \( F(x) = 10.5 - 0.8x \), set the equation to zero:

• Step 1: \( 0 = 10.5 - 0.8x \)
• Step 2: Rearrange to find \( x \): \( 0.8x = 10.5 \)
• Step 3: Solve for \( x \): \( x = \frac{10.5}{0.8} \)

In this example, the x-intercept is at \( (13.125, 0) \), showing that the graph crosses the x-axis at the point \( x = 13.125 \). Understanding the x-intercept helps in predicting where the function hits the x-axis without needing to plot every single point.

The y-intercept is crucial for graphing linear functions as it indicates where the graph intersects the y-axis. At this point, the x-value is zero because the intercept occurs directly on the y-axis. This simplifies finding the y-intercept: just substitute \( x = 0 \) into the function.

For example, with our function \( F(x) = 10.5 - 0.8x \), finding the y-intercept works like this:

• Step 1: Substitute \( x = 0 \) into the function: \( F(0) = 10.5 - 0.8 \times 0 \)
• Step 2: Simplify to find the y-value: \( F(0) = 10.5 \)

Thus, the y-intercept is \( (0, 10.5) \), meaning the graph crosses the y-axis at 10.5.

It makes it easier to start the graphing process, providing a spot on the graph to help align the rest of the points along the linear path.

Graphing linear equations involves plotting points on a graph to represent the solutions of the equation. When graphing a linear function like \( F(x) = 10.5 - 0.8x \), the process is straightforward, as all solutions fall along a straight line.

First, identify the x- and y-intercepts. These points are often the easiest to find and essential for accurately graphing the line. Once you've got the points \( (13.125, 0) \) for the x-intercept and \( (0, 10.5) \) for the y-intercept, mark these on the coordinate plane.

Draw a straight line through these points, ensuring it extends in both directions beyond the intercepts. This line fully represents all the solutions to the equation \( F(x) = 10.5 - 0.8x \). Remember, linear equations have a constant slope, making them appear as straight lines.

• A simple reminder: the slope tells us the direction and steepness of the line.
• The negative sign in \(-0.8x\) indicates the line will slope downward from left to right.

By connecting the intercepts with a straight line, you have successfully graphed the linear equation!