how do i tell if my graph is linear or nonlinear...

Linear means the points lie on a straight line.

If you are given the (x,y) coordinates of points, then you can proceed as follows:

Say you are given these four points. Is the graph of these points linear?
(1,1) (2,2) (3,3) (4,5)

First fit a line to two of the points (any two, I will take the first two)

y = 1 x + 0 or y = x goes through the first two. (I will let you figure out why :)
Now if the other two points are on that line, the graph is linear.
So try the third point
3 = 3 sure enough, so the graph of the first three points would be linear, but the fourth has to be on the line as well.
5 = 4 Whoops, no, that point does not fit our line at all! Therefore the graph of the four points is NOT linear.

To determine whether a graph is linear or nonlinear, you need to understand the characteristics of both types.

A linear graph represents a straight line and follows a linear equation of the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.

On the other hand, a nonlinear graph does not follow a straight line and cannot be represented by a linear equation.

Here are the steps to determine if a graph is linear or nonlinear:

1. Examine the graph: Look at the shape of the graph and observe if it appears to be a straight line or not. If it is a straight line, it is likely linear.

2. Check for a constant rate of change: Select two points on the graph and calculate the rate of change between them. If the rate of change (slope) remains the same for all pairs of points on the graph, then it is linear. A constant slope indicates a linear relationship.

3. Use the equation: If you have an equation that represents the graph, check if it fits the form of a linear equation (y = mx + b). If it does, the graph is linear. If not, it is nonlinear.

4. Test various points: You can select random points on the graph and check if they fall on a straight line. Linear graphs will have all points connected by a straight line, while nonlinear graphs will not.

Remember, these steps are not foolproof, and more complex graphs may require additional analysis. However, they should provide a good starting point in determining if your graph is linear or nonlinear.