How To Find The Slope

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:

1. Choose two points on the line.
2. Calculate the change in y between the two points.
3. Calculate the change in x between the two points.
4. 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:

1. Put the equation in slope-intercept form (y = mx + b).
2. 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.