To graph the linear equation $y = 5x + 2$, start by selecting several values for $x$ and calculating the corresponding $y$ values.

To begin plotting the equation, choose simple integer values for $x$. A good starting set includes $-2, -1, 0, 1,$ and $2$. For each selected $x$ value, substitute it into the equation to determine the corresponding $y$ value.

Let’s illustrate this with a few examples:

1. For $x = 0$:

   $$y = 5(0) + 2 = 2$$

   This gives us the point $(0, 2)$.

2. For $x = 1$:

   $$y = 5(1) + 2 = 7$$

   This results in the point $(1, 7)$.

3. For $x = -1$:

   $$y = 5(-1) + 2 = -3$$

   This yields the point $(-1, -3)$.

After calculating these values, you will have the following set of coordinates: $(0, 2)$, $(1, 7)$, and $(-1, -3)$. You can now plot these points on a graph with the $x$-axis and $y$-axis. Once you’ve plotted at least two points, you can draw a straight line through them, as the equation $y = 5x + 2$ describes a linear relationship.

Keep in mind that plotting more points can enhance the accuracy of your line. However, for linear equations, two points are sufficient to define the line. This method effectively helps you visualize the relationship between $x$ and $y$ as described by the equation.