How to Write Linear Equations? (+FREE Worksheet!)

Related Topics

• How to Find Midpoint
• How to Find Slope
• How to Graph Linear Inequalities
• How to Find Distance of Two Points
• How to Graph Lines by Using Standard Form

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: \(-2=(6)(1)+b → -2=6+b \)
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: \(y=-x+b \)
\((1,1) →1=-1+b→ 1+1=b → b=2\)
\((-1,3)→3=-(-1)+b→3-1=b → b=2\)
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: \(-2=(7)(2)+b → -2=14+b \)
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: \(y= -x+b \)
\( (2,1) →1=-2+b→1+2=b → b=3\)
\( (-1,4)→4=-(-1)+b→4-1=b → b=3\)
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. \(\color{blue}{y =\space – x – 2}\)
4. \(\color{blue}{y =\space –5x – 4}\)
5. \(\color{blue}{y = x + 3}\)
6. \(\color{blue}{y =\space – 5x + 2}\)