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More Lessons for Geometry

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In this lesson, we will learn

### Slope of a line

**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 Formula

**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:

1. Find the slope of the line containing the points (-10,-4) and (-15,-6)

2. Find the slope for (4,8) and (-7,8)

3. Find the slope for (6,-9) and (6,-10)

### Y-intercept

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Geometry

Math Worksheets

In this lesson, 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.

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.

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 = * =

To solve the problem (without graphing), we can use the slope formula, which states that

Example:

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

It shows that the slope can be zero or undefined.

Example:

1. Find the slope of the line containing the points (-10,-4) and (-15,-6)

2. Find the slope for (4,8) and (-7,8)

3. 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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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