**How to find slope of straight line:** The slope of a line is a measure of the incline of the line. A positive slope indicates a line that goes UP from left to right. This line has a positive slope.

A negative slope indicates that a line goes DOWN if you are moving from left to right. This line has a negative slope.

## Why slope of a line?

Knowing the value for the slope of a line is necessary when writing its equation. And also, the slope of a line indicates how to step the line is.

So, knowing how to find the slope of a line is an important skill for higher Geometry and Algebra concepts.

## How to find the slope of a line?

There are two common ways to find the slope of a line.

- 1. Slope-intercept method (Using the general equation of a straight line, y = mx + c)
- 2. Using the two-points method.

**Method 1: Slope-intercept method**

To change an equation to slope-intercept form, make y the subject of the equation so that the equation is in the form y = mx + c.

Follow these two steps:

Step 1: Solve the equation for y (i.e. make y the subject)

Step 2: The variable in front of the x (referred to as m) is the slope.

Example: Find the slope of the line 2x + y − 2 = 0.

Step 1: Solve the equation 2x + y − 2 = 0 for y.

- 2x + y − 2 = 0 for y.(Subtract 2x from both sides of the equation)
- y − 2 = −2 x (Add 2 to both sides of the equation)
- y = −2x + 2 (Now, this is in the form y = mx + c)

Step 2: The number in front of x is the slope.

- −2 is in front of x, so −2 is the slope.

**Quick hits #1: Change each of the following equations to slope-intercept form and find the slope.**

1. 5x − y + 2 = 0

2. 4x + 2y = −8

3. 7y = −3x

4. x + 2y = 1

The answers are at the end of this article.

## Method 2: Two-points method (find slope between two points)

To find the slope of a line using the point-point method, just find two points on the line.

Step 1: Find two points on the line.

Step 2: Find the change in y: Subtract the first y-coordinate (y_{1}) from the second y-coordinate (y_{2}).

y_{2} – y_{1}

Step 3: Find the change in x: Subtract the first x-coordinate ( x_{1}) from the second x-coordinate ( x_{2}).

x_{2} -x_{1}

Step 4: Divide the change in y (Step 2) by the change in x (Step 3). The answer is the slope of the line.

Slope = (y_{2} – y_{1})/ ( x_{2} -x_{1})

Example: Find the slope of a line through the points (3, 2) and (7, 1).

- 1: Find two points on the line. Two points on the line are given (3, 2) and (7, 1).
- 2: Find the change in y 2. − 1 = 1
- 3: Find the change in x 3. − 7 = −4
- 4: Find the slope of the line by dividing the change in y (Step 2) by the change in x (Step 3).

^{1}/_{(−4)}=^{− 1}/_{4}. The slope is^{− 1}/_{4}

**Quick hits#2: Find the slope of the line through the following points.**

1. (3, 0) and (0, −2)

2. (7, 1) and (2, 6)

3. (0, 0) and (5, 3)

4. (−3, −2) and (1, 1)

The answers are at the end of this article.

Check out ourfree maths worksheets here and download them. If you have a question, leave a comment and we will get back to you.

## 10 common questions about slope

**1. Is slope also called gradient? **

A. Yes

**2. What is the slope of a straight line?**

A. The slope of a line is a measure of the incline of the line.

**3. What is the slope of a line formula?**

A. The formula of a slope is given the ‘change is y’ (the RISE) divide by ‘change is x’ (the RUN).

Slope = ^{RISE (change in y)}/_{RUN (change in x) }

**4. What is the slope of the line parallel to the x-axis?**

A. Slope = 0.

There is no (zero) rise. Slope = 0/_{RUN} = 0

**5. What is the slope of the line parallel to the y-axis?**

A. No slope.

(The slope is undefined. Slope = ^{RISE}/_{RUN } = ^{RISE}/0_{ } = undefined)

**6. What is the slope of a horizontal (flat) line?**

A. Slope = 0

A flat line is also called the line parallel to x-axis.

**7. What is the slope of a vertical line?**

A. No slope

A vertical line is also called ‘the line parallel to the x-axis.

**8. How can I find the slope of a straight line?**

A. There are two ways of finding the slope of a straight line: By using the slope-intercept form, y = mx + c; or the Two-points method.

**9. How can I identify slope in the equation y = mx + c?**

A. m in the equation represents the slope.

**10. How to find the slope of a line with two points?**

A. Use the point-point method to work out the slope of a line given two points.

## Free Online Mathematics Worksheets

We are compiling maths worksheets that we thought will be useful. Download this article as a worksheet: **find out how to find the slope of a straight line**.

**10 common decimals:** We collected the 10 fractions, percentages, and decimals that are commonly used in assessments, tests and exams.

Decimal | Fraction | Percentage |
---|---|---|

0.1 | ¹/10 | 10% |

0.125 | ⅛ | 12.5% |

0.2 | ⅕ | 20% |

0.25 | ¼ | 25% |

33.3… | ⅓ | 33⅓% |

0.4 | ⅖ | 40% |

0.5 | ⅔ | 66⅔% |

0.6 | ½ | 50% |

66.6… | ⅗ | 60% |

0.75 | ¾ | 75% |

**Quick hits #1 Answers**

1. y = 5x + 2, slope = 5

2. y = −2x − 4, slope = −2

3.y = − 3 7 x, slope = − 3

4. y = −^{1}/_{2} x + ^{1}/_{2} , slope = 1 2

**Quick hits #2 Answers**

1. ^{ 2}/_{3} 2. −1 3. ^{3}/_{5} 4. ^{3}/_{4}