Slope From a Graph

Slope from a graph

The slope tells you how steep a line is. On a graph, it compares the vertical change to the horizontal change between two points.

1) Pick two clear points

Choose two points on the line where the graph crosses grid intersections if possible. Read each point carefully as ((x_1, y_1)) and ((x_2, y_2)).

2) Find the change in y and the change in x

Use the slope idea:

• rise = (y_2 - y_1)
• run = (x_2 - x_1)

Then write the slope as [ m = \frac{y_2 - y_1}{x_2 - x_1} ]

3) Simplify the fraction

Reduce the fraction if possible. If the line goes down as you move right, the slope will be negative. If it goes up, the slope will be positive.

4) Check your answer

Make sure your sign matches the graph:

• rising left to right → positive slope
• falling left to right → negative slope
• horizontal line → slope (0)
• vertical line → slope is undefined

A quick check is to count the same number of squares every time you move horizontally and vertically. If your fraction matches that pattern, your slope is correct.