How do I plot a point when the grid intervals are not labeled one by one?

First work out what one grid interval represents on each axis. Look at two labeled values on the x-axis, count the equal spaces between their grid lines, and divide the change in value by that count. Repeat independently for the y-axis; the two axes do not have to use the same increments. [S1]

For example, suppose the x-axis labels 0 and 12 are six grid intervals apart. Each interval represents 2 units. If the y-axis labels 0 and 4 are four intervals apart, each represents 1 unit. These numbers are an example, not a claim about your particular graph. For (6, 4), count three x-intervals from zero and four y-intervals from zero. The point is where those positions meet: move along x first, then up along y. A coordinate names its horizontal x-value followed by its vertical y-value. [S1]

Use zero and the visible labeled value if both are on that same axis. Count the grid intervals from zero to the labeled value, then divide that value by the interval count. For instance, if a label 10 is five equal intervals from zero, each interval represents 2 units. That conclusion depends on the grid spaces being equal and the label actually being on the line you counted.

If zero is not visible, use any two labeled values on that axis and find their difference. If there is no pair of usable labels, the scale cannot be determined reliably from the visible information alone. Don’t guess an interval size; look for a clearer copy or ask for the axis scale.

Check each axis on its own. Starting at one labeled grid line, count the spaces—not the lines—to the next labeled grid line. Your proposed value per space should take you exactly from the first label to the second. For example, a change of 8 over four spaces means 2 units per space. If your count would land short or go past the next label, recount the spaces or revisit the arithmetic. [S1]

Then check your plotted point in both directions: its horizontal position should match x, and its vertical position should match y. The point should sit at the intersection of the chosen vertical and horizontal grid positions. Do not transfer the x-axis interval size to the y-axis unless the labels show that it is the same.

Suppose your graph shows x-axis labels 0 and 8 with four equal spaces between them, and y-axis labels 0 and 6 with three equal spaces between them. The x scale is 8 ÷ 4 = 2 units per space; the y scale is 6 ÷ 3 = 2 units per space. For the point (6, 4), count three spaces right from zero on x and two spaces up from zero on y. Mark their intersection.

Copyable check:

1. x: labeled change ___ ÷ spaces ___ = ___ units per space.
2. y: labeled change ___ ÷ spaces ___ = ___ units per space.
3. Point (x, y): x needs ___ spaces; y needs ___ spaces.
4. Check each count against the next labeled value.

This method determines positions from the labels and equal intervals. It does not establish coordinates if the graph is distorted, the grid spacing is unequal, or the axis labels are missing or unclear.