# 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.

**The Absolute Best Books to Ace Pre-Algebra to Algebra II**

### 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 Best Book to Help You Ace**** Pre-Algebra**

### 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 Greatest Books for Students** **to Ace the Algebra**

## Related to This Article

### More math articles

- Reveal the Secrets: “TSI Math for Beginners” Detailed Solution Manual
- How to Find Missing Angles of Triangles
- Infinitely Close But Never There
- TASC Math FREE Sample Practice Questions
- ALEKS Math Placement Review and FAQs
- Introduction to Complex Numbers: Navigating the Realm Beyond the Real
- The World of Separable Differential Equations
- How to Pass TSI Test: Top Tips and Key Tactics
- Top 10 4th Grade MAP Math Practice Questions
- How to Use Box Multiplication Method

## What people say about "How to Find Slope? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.