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Graphing linear equations is a fundamental skill in algebra. A linear equation in two variables, such as the one given in the example, produces a straight line when graphed on the coordinate plane. The general form for these equations is ax + by = c where a, b, and c are constants. To graph a linear equation, we use its intercepts and slope. The intercepts provide points where the line crosses the axes, while the slope shows the steepness and direction of the line. In the given exercise, the equation is 4x - y = 0. This can be simplified to y = 4x, indicating a slope of 4 passing through the origin.

By plotting just a couple of points like the intercepts and another value, we can accurately draw the line. The advantage of knowing how to quickly find and use these intercepts is that it makes the graphing process much easier and more intuitive.

The coordinate plane is a two-dimensional surface where we plot points, lines, and curves. It consists of two perpendicular lines known as the x-axis (horizontal) and y-axis (vertical). These axes divide the plane into four quadrants. Each point on the plane is identified by an ordered pair (x, y). The first number (x-coordinate) specifies horizontal position, while the second number (y-coordinate) specifies vertical position.

In the given exercise, we plotted the points (0,0) and (1,4) on the coordinate plane to draw the line representing the equation 4x - y = 0. The intercepts we found help us understand where the line crosses each axis. Remember, starting with the origin, where both x and y are zero, is often the simplest step when graphing lines that cross through it.

Finding intercepts is one of the first steps in graphing linear equations. Intercepts are where the graph of an equation crosses the axes:

• The x-intercept is where the graph meets the x-axis (y=0).
• The y-intercept is where the graph meets the y-axis (x=0).

For the equation 4x - y = 0, we found both intercepts by setting one variable to 0 and solving for the other.

To find the x-intercept:

• Set y = 0 in the equation.
• Solve for x. This gave us (0,0) for the x-intercept.

To find the y-intercept:

• Set x = 0 in the equation.
• Solve for y. This also gave us (0,0) for the y-intercept.

Since both intercepts are the same, we used another point, (1,4), to better define our line. Finding these points helps ensure we draw our line accurately on the coordinate plane.