Worksheet for calculating the distance between two points on a coordinate plane.

To find the distance between two points on a graph, we use the distance formula. Here is the step-by-step solution for the points $(8, 8)$ and $(3, 5)$.

Step 1: Identify the coordinates.
Let point 1 be $(x_1, y_1) = (8, 8)$
Let point 2 be $(x_2, y_2) = (3, 5)$

Step 2: Use the distance formula.
The formula is:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Step 3: Substitute the values into the formula.
$$d = \sqrt{(3 - 8)^2 + (5 - 8)^2}$$

Step 4: Subtract the numbers inside the parentheses.
$$3 - 8 = -5$$
$$5 - 8 = -3$$

So the equation becomes:
$$d = \sqrt{(-5)^2 + (-3)^2}$$

Step 5: Square the results.
$$(-5)^2 = 25$$
$$(-3)^2 = 9$$

Now add them together:
$$d = \sqrt{25 + 9}$$
$$d = \sqrt{34}$$

Step 6: Simplify.
The number 34 cannot be simplified further because it has no perfect square factors (other than 1). So, the exact answer is $\sqrt{34}$.

If you need a decimal approximation:
$\sqrt{34} \approx 5.83$

Final Answer:
\sqrt{34}