Question

How can you use an equation to make a prediction from a pattern?

Answer 1

when you find the equation of a line, a linear equation, all the values increase or decrease in a straight line, like either one of these:

Answer 2

All the little dots I made on the lines in both will fit perfectly into a linear equation. When you know the equation of a line, you can be given either an x value to use to solve for y, or you can be given a y value to solve for x. Like if I told you the equation of a line is
y = 3x+1, you know that if x is 1, then y will be 4. If x is 2, y will be 7. These are points on the line y = 3x+1. So if I give you an x value of 5, you can use your equation to find out what the resulting y value will be. That's how you use equations for predictions. You have to know the equation first, though, for this to work. Or you have to be able to find out what the equation is from a graphed line. That's about it for that. I hope you understand!