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

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

- 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.

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### 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 point. 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 \(y=7x-16\).

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### Writing Linear Equations – Example 4:

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

**Solution:**

Slop \(= \frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{4- 1}{-1- 2}=\frac{3}{-3}=-1 → m= -1\)

You can use either point to find the value of \(b\). 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.

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

### Download Writing Linear Equations Worksheet

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

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