Decide on the range of x values that you want to include. Although this range depends on the function, it is usually good to include negative and positive values. It is also good to include values for which the value inside the absolute value bars is negative and positive. You may need to try a few ranges. In the example, of y = |5x + 2| you could choose -3 to +3.
Make tick marks on the x-axis at several numbers inside the range you chose. In the example, you could mark -3, -2, -1, 0, 1, 2 and 3.
Calculate the function at those points. In the example when x = -3, y = |5*(-3) + 2| = |-15 + 2| = |-13| = 13. At x = -2, y = |5*(-2) + 2| = |-10 + 2| = |-8| = 8. Similarly , at x = -1, y = 2; at x = 0, y = 2; at x = 1, y = 7; at x = 2, y = 12 and at x = 3, y = 17.
Plot those points on your graph.
Connect the points with smooth lines.