In these lessons, we will learn

- how to find the slope of a line from the graph using rise over run.
- how to find the slope of a line using the slope formula.
- how to find the y-intercept from the graph.

**Related Pages**

Calculating Slope

More Lessons for Geometry

Math Worksheets

The slant of a line is called the slope. Slope describes how steep a line is. The slope of a line can be found using the ratio of rise over run between any two points on the line.

In the following graph, the rise from point P to point Q is 2 and the run from point P to point Q is 4.

Take note that the slope obtained would be the same no matter which two points on the line were selected to determine the rise and the run.

A horizontal line has a slope of zero. A vertical line has an undefined slope.

A line with a positive slope slant upwards, whereas a line with a negative slope slant downwards.

**How to find the slope of a line using the ratio of rise over run between any two points on the line?**

**How to calculate the slope of a line using the rise over run method?**

It also explains positive slope, negative slope, and the slope of horizontal and vertical lines.

Slope can also be calculated as the ratio of the change in the y-value over the change in the x-value.

Given any two points on a line, (x_{1}, y_{1}) and (x_{2}, y_{2}), we can calculate the slope of the line by using this formula:

For example: Given two points, P = (0, –1) and Q = (4,1), on the line we can calculate the slope of the line.

*slope* = =

Let’s look at a line that has a negative slope.

For example: Consider the two points, R(–2, 3) and S(0, –1) on the line. What would be the slope of the line?

*slope* = =

**How to find the slope of the line that passes through two points when given the coordinates of the points?**

To solve the problem (without graphing), we can use the slope formula, which states that m = (y_{2} − y_{1}) / (x_{2} − x_{1}). The slope formula can be read as “slope equals the second y-coordinate minus the first y-coordinate over the second x-coordinate minus the first x-coordinate”.

**Example:**

Find the slope of the line passing through the points (5,4) and (8,6)

**How to use the slope formula to find the slope of a line given the coordinates of two points on the line?**

It shows that the slope can be zero or undefined.

**Example:**

- Find the slope of the line containing the points (-10,-4) and (-15,-6)
- Find the slope for (4,8) and (-7,8)
- Find the slope for (6,-9) and (6,-10)

The y-intercept is where the line intercepts (meets) the y-axis.

In the following diagram, the line intercepts the y-axis at (0,–1). Its y-intercept is equal to –1.

Equation of a straight line can be written in slope-intercept form.

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