## How to Find the Slope of a Line

The slope of a line is a measure of its steepness. It is calculated by dividing the change in y by the change in x between any two points on the line. The slope can be positive, negative, zero, or undefined.

**Positive Slope**

A line with a positive slope is rising from left to right. The greater the slope, the steeper the line.

**Negative Slope**

A line with a negative slope is falling from left to right. The greater the slope, the steeper the line.

**Zero Slope**

A line with a zero slope is horizontal. It does not rise or fall from left to right.

**Undefined Slope**

A line with an undefined slope is vertical. It does not have a defined x-intercept.

### How to Find the Slope Using the Slope Formula

The slope of a line can be calculated using the following formula:

`slope = (y2 - y1) / (x2 - x1)`

where (x1, y1) and (x2, y2) are any two points on the line.

### Example

Find the slope of the line that passes through the points (2, 3) and (5, 7).

```
slope = (7 - 3) / (5 - 2)
slope = 4 / 3
```

Therefore, the slope of the line is 4/3.

### Applications of Slope

The slope of a line can be used to:

- Determine the direction of a line
- Calculate the rate of change of a variable
- Determine the angle of a line
- Classify lines as parallel, perpendicular, or neither

### FAQs

**Q: What is the difference between slope and gradient?**

A: Slope and gradient are two terms that are used interchangeably to refer to the steepness of a line.

**Q: Can a line have more than one slope?**

A: No, a line can only have one slope.

**Q: What is the slope of a vertical line?**

A: The slope of a vertical line is undefined.

**Q: What is the slope of a horizontal line?**

A: The slope of a horizontal line is zero.

**Q: How can I find the slope of a line from a graph?**

A: To find the slope of a line from a graph, you can use the following steps:

- Choose two points on the line.
- Calculate the change in y between the two points.
- Calculate the change in x between the two points.
- Divide the change in y by the change in x.

The result will be the slope of the line.

**Q: How can I find the slope of a line from an equation?**

A: To find the slope of a line from an equation, you can use the following steps:

- Put the equation in slope-intercept form (y = mx + b).
- The coefficient of x (m) is the slope of the line.

**Q: What is the slope of a line that is parallel to another line?**

A: Lines that are parallel have the same slope.

**Q: What is the slope of a line that is perpendicular to another line?**

A: Lines that are perpendicular have slopes that are negative reciprocals of each other.