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.

## 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.

### 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 \(y=6x-8\).

### 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: \(y=-x+2\)

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

### 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

### 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

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