To find the slope of a line on a graph, follow these steps:

1. Select Two Points on the Line
   Choose any two points on the line, preferably points with integer coordinates for easier calculation. Label them as (x1,y1)(x_1,y_1)(x1​,y1​) and (x2,y2)(x_2,y_2)(x2​,y2​)

2. Calculate the Rise and Run

   • Rise is the vertical change between the two points: y2−y1y_2-y_1y2​−y1​.

   • Run is the horizontal change between the two points: x2−x1x_2-x_1x2​−x1​.
     Note the direction:

   • Rise is positive if you move up, negative if you move down.

   • Run is positive if you move right, negative if you move left

3. Use the Slope Formula
   Calculate the slope mmm using the formula:

m=riserun=y2−y1x2−x1m=\frac{\text{rise}}{\text{run}}=\frac{y_2-y_1}{x_2-x_1}m=runrise​=x2​−x1​y2​−y1​​

This ratio represents the steepness of the line

4. Interpret the Slope
   • A positive slope means the line rises as it moves from left to right.
   • A negative slope means the line falls as it moves from left to right.
   • A slope of zero means the line is horizontal.
   • An undefined slope (division by zero) means the line is vertical

Example:
If you pick points (0,−3)(0,-3)(0,−3) and (5,1)(5,1)(5,1), the rise is 1−(−3)=41-(-3)=41−(−3)=4 and the run is 5−0=55-0=55−0=5. So the slope is 4/54/54/5

. This method works for any straight line on a graph and helps you understand how steep the line is

Summary

• Pick two points on the line.
• Calculate rise (change in y) and run (change in x).
• Divide rise by run to get the slope.

This is the standard way to find slope from a graph.