How to Find Slope? (+FREE Worksheet!)
The slope of a line shows the direction of the line. In this article, you learn how to find the slope of a line.

Related Topics
- How to Find Midpoint
- How to Find Distance of Two Points
- How to Graph Linear Inequalities
- How to Write Linear Equations
- How to Graph Lines by Using Standard Form
Step by step guide to finding slope
- The slope of a line represents the direction of a line on the coordinate plane.
- A coordinate plane contains two perpendicular number lines. The horizontal line is \(x\) and the vertical line is \(y\). The point at which the two axes intersect is called the origin. An ordered pair \((x, y)\) shows the location of a point.
- A line on the coordinate plane can be drawn by connecting two points.
- To find the slope of a line, we need two points.
- The slope of a line with two points A \((x_{1},y_{1})\) and B \((x_2,y_2)\) can be found by using this formula: \(\color{blue}{\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1}} =\frac{rise}{run}}\)
- We can also find the slope of a line when we have its equation. The equation of a like is usually written in the form of \(y=mx+b\), where \(m\) is the slope of the line and \(b\) is the \(y\)-intercept.
Best Algebra Prep Resource
Finding Slope – Example 1:
Find the slope of the line through these two points: \((1,–9)\) and \((2,5) \).
Solution:
Slope \(=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }\). Let \((x_{1},y_{1} )\) be \((1,- \ 9) \) and \((x_{2},y_{2} )\) be \((2,5)\). Then: slope \(=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }=\frac{5 \ – \ (- \ 9)}{2 \ – \ 1}=\frac{5 \ + \ 9}{1}=\frac{14}{1}=14\)
Finding Slope – Example 2:
Find the slope of a line with these two points: \((6,1)\) and \((-2,9)\).
Solution:
Slope \(=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }\). Let \((x_{1},y_{1} )\) be \((6,1) \) and \((x_{2},y_{2} )\) be \((-2,9)\). Then: slope \(=\frac{y_{2} \ – \ y_{1}}{x_{2} \ – \ x_{1} }=\frac{9 \ – \ 1}{- \ 2 \ – \ 6}=\frac{8}{-8}=\frac{1}{-1}=\ – \ 1\)
Finding Slope – Example 3:
Find the slope of a line with these two points: \((2,–10)\) and \((3,6)\).
Solution:
Slope \(=\frac{y_{2}- y_{1}}{x_{2 } – x_{1 }}\). Let \((x_{1},y_{1} )\) be \((2,-10) \) and \((x_{2},y_{2} )\) be \((3,6)\). Then: slope \(=\frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{6-(-10)}{3 – 2}=\frac{6+10}{1}=\frac{16}{1}=16\)
The Absolute Best Book to Ace the College Algebra Course
Finding Slope – Example 4:
Find the slope of the line with equation \(y=3x+6\)
Solution:
when the equation of a line is written in the form of \(y=mx+b\), \(m\) is the slope of the line. Then, in this line with equation \(y=3x+6\), the slope is \((3)\) .
Exercises for Finding Slope
Find the slope of the line through each pair of points.
- \(\color{blue}{(1, 1), (3, 5)}\)
- \(\color{blue}{(4, – 6), (– 3, – 8)}\)
- \(\color{blue}{(7, – 12), (5, 10)}\)
- \(\color{blue}{(19, 3), (20, 3)}\)
- \(\color{blue}{(15, 8), (– 17, 9)}\)
- \(\color{blue}{(6, – 12), (15, – 3)}\)
Download the Finding Slope Worksheet

Answers
- \(\color{blue}{2}\)
- \(\color{blue}{\frac{2}{7}}\)
- \(\color{blue}{-11}\)
- \(\color{blue}{0}\)
- \(\color{blue}{-\frac{1}{32}}\)
- \(\color{blue}{1}\)
The Best Books for Ace College Algebra
Related to This Article
More math articles
- How to Find Even and Odd Functions?
- Number Properties Puzzle – Challenge 18
- 3rd Grade OST Math Worksheets: FREE & Printable
- FREE 8th Grade ACT Aspire Math Practice Test
- The Ultimate 6th Grade FSA Math Course (+FREE Worksheets)
- CBEST Test Facts and FAQs
- What’s A Good ACT Score?
- What is Rationalizing Infinite Limits: Useful Techniques to Simplify Limits
- FREE ISEE Middle Level Math Practice Test
- FREE 7th Grade PSSA Math Practice Test
What people say about "How to Find Slope? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.