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Understanding how to solve algebraic equations is fundamental in graphing linear equations. In this case, the equation presented is a simple linear equation involving a single variable, y. The core principle of solving such equations is to isolate the variable on one side of the equation. This is usually accomplished by performing the same mathematical operation on both sides. Here's how:
To solve the equation 5y = 20, we divide both sides by 5, which is the coefficient of y. Simplified, this gives us y = 20 / 5. When you divide the constant term 20 by the coefficient 5, you get y = 4. This answer is the first critical step, as it will be used to graph the solution on the coordinate plane.
Always remember that whatever operation you apply to one side, you must also apply to the other to maintain the equation's balance. This method is not just for simple equations but is also the starting point for more complex algebraic problems.

The horizontal line equation is a type of linear equation where the value of y is constant no matter what the value of x is. It has the general form y = k, where k is a real number. The graph of such an equation is a horizontal line that crosses the y-axis at the point (0, k).
For the given equation y = 4, the line will cross the y-axis at the point where y equals 4. This is because all the points on the line have the same y-coordinate, which is 4 in this case. Regardless of the x-value, whether it be 1, 10, or -5, the y-value remains 4. This is characteristic of horizontal lines – their slope is zero since there is no change in y as x increases or decreases.

Graphing on the coordinate plane involves plotting points that satisfy an equation, and then connecting those points to reveal the shape of the equation's graph. Each point on the plane is identified by an ordered pair of numbers, known as coordinates. The first number, x, indicates the position along the horizontal axis, and the second number, y, indicates the position along the vertical axis.
The process of graphing begins with identifying key points that fit the equation. For horizontal and vertical lines, this is relatively straightforward since either the x or y value remains constant. In the example y = 4, any point with y equals 4 is on the line. You can select various x-values, such as -2, 0, 2, and 4, pair them with y = 4, and mark these points on the graph: (-2, 4), (0, 4), (2, 4), (4, 4). Then, simply draw a straight line through these points to complete the graph of the equation.