The gradient and intercept of a line can easily be stated by looking carefully at its equation.

For the line with equation y = mx + c, the gradient is m and the intercept on

the *y-axis* is c.

m is the coefficient of x **when in the form y = ......**

c is the number on its own

**Example**

State the gradient and intercept of the line with equation:

y - 1 | = | x |

2 |

**Answer**

y - 1 | = | x |

2 |

Multiply both sides by 2 to get

y - 1 = 2x

Rearrange the equation to make y the subject by adding 1 to both sides.

y = 2x + 1

Comparing y = 2x + 1 to y = mx + c, we see that m = 2 and c = 1

The gradient of the line, m, is **2** and the intercept, c, is **1**, which means that it crosses the y-axis at (0, 1)

**Check**

The line is shown below.

** y = 2x + 1**

**Note **

The equation y = 2x + 1 can be rewritten in several ways as shown below.

They all represent the SAME line.

y = 1 + 2x

y - 1 = 2x

x = ½ (y - 1)