How to Write Linear Equations

How to Write Linear Equations

In this article, you learn how to write the equation of the lines by using their slope and one point or using two points on the line.

Related Topics

Step by step guide to writing linear equations

  • The equation of a line in slope intercept form is: \(\color{blue}{y=mx+b}\)
  • Identify the slope.
  • Find the \(y\)–intercept. This can be done by substituting the slope and the coordinates of a point \((x, y)\) on the line.

Writing Linear Equations – Example 1:

What is the equation of the line that passes through \((1, -2)\) and has a slope of \(6\)?

Solution:

The general slope-intercept form of the equation of a line is \(y=mx+b\), where m is the slope and b is the \(y\)-intercept.
By substitution of the given point and given slope, we have: \(-2=(1)(6)+b \)
So, \(b= -2-6=-8\), and the required equation is \(y=6x-8\).

Writing Linear Equations – Example 2:

Write the equation of the line through \((1, 1)\) and \((-1, 3)\).

Solution:

Slop \(= \frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{3- 1}{-1- 1}=\frac{2}{-2}=-1 → m=-1\)
To find the value of b, you can use either points. The answer will be the same: \(y=-x+b \)
\((1,1) →1=-1+b→b=2\)
\((-1,3)→3=-(-1)+b→b=2\)
The equation of the line is: \(y=-x+2\)

Writing Linear Equations – Example 3:

What is the equation of the line that passes through \((2,–2)\) and has a slope of \(7\)?

Solution:

The general slope-intercept form of the equation of a line is \(y=mx+b\), where \(m\) is the slope and \(b\) is the \(y-\)intercept.
By substitution of the given point and given slope, we have: \(-2=(7)(2)+b \)
So, \(b= –2-14=\ -16\), and the required equation is \(y=7x-16\).

Writing Linear Equations – Example 4:

Write the equation of the line through \((2,1)\) and \((-1,4)\).

Solution:

Slop \(= \frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{4- 1}{-1- 2}=\frac{3}{-3}=\ -1 → m= \ -1\)
To find the value of b, you can use either points. The answer will be the same: \(y= \ -x+b \)
\( (2,1) →1=-2+b→b=3\)
\( (-1,4)→4=-(-1)+b→b=3\)
The equation of the line is: \(y= \ -x+3\)

Exercises for Writing Linear Equations

Write the slope–intercept form of the equation of the line through the given points.

  1. \(\color{blue}{through: (– 4, – 2), (– 3, 5)}\)
  2. \(\color{blue}{through: (5, 4), (– 4, 3) }\)
  3. \(\color{blue}{through: (0, – 2), (– 5, 3) }\)
  4. \(\color{blue}{through: (– 1, 1), (– 2, 6) }\)
  5. \(\color{blue}{through: (0, 3), (– 4, – 1) }\)
  6. \(\color{blue}{through: (0, 2), (1, – 3) }\)

Download Writing Linear Equations Worksheet

  1. \(\color{blue}{y = 7x + 26}\)
  2. \(\color{blue}{y = \frac{1}{9} x + \frac{31}{9}}\)
  3. \(\color{blue}{y = – x – 2}\)
  4. \(\color{blue}{y = – 5x – 4}\)
  5. \(\color{blue}{y = x + 3}\)
  6. \(\color{blue}{y = – 5x + 2}\)

Related to "How to Write Linear Equations"

Top 10 Tips to ACE the CBEST Math Test
Top 10 Tips to ACE the CBEST Math Test
Top 10 Tips You MUST Know to Retake the CBEST Math
Top 10 Tips You MUST Know to Retake the CBEST Math
Top 10 Tips to Overcome CBEST Math Anxiety
Top 10 Tips to Overcome CBEST Math Anxiety
Top 10 Tips to Create a CBEST Math Study Plan
Top 10 Tips to Create a CBEST Math Study Plan
How is the CBEST Test Scored?
How is the CBEST Test Scored?
Top 10 Tips You MUST Know to Retake the PERT Math
Top 10 Tips You MUST Know to Retake the PERT Math
Top 10 Tips to Overcome PERT Math Anxiety
Top 10 Tips to Overcome PERT Math Anxiety
Top 10 Tips to Create a PERT Math Study Plan
Top 10 Tips to Create a PERT Math Study Plan
Top 10 Tips You MUST Know to Retake the ASTB-E Math
Top 10 Tips You MUST Know to Retake the ASTB-E Math
Top 10 Tips to Overcome ASTB Math Anxiety
Top 10 Tips to Overcome ASTB Math Anxiety

Leave a Reply

Your email address will not be published. Required fields are marked *

36% OFF

Download Instantly

X

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…