How to tell if an equation is linear

From the table:

The x and y values change at a
constant rate

Linear | Nonlinear | |||

x | y | x | y | |

-1 | 5 | 0 | 0 | |

0 | 7 | 1 | 1 | |

1 | 9 | 2 | 4 | |

2 | 11 | 3 | 9 | |

3 | 13 | 4 | 16 |

From the graph:

It is a straight line.

From the equation:

It is in the
form: y = mx + b

How to tell if an equation is increasing or decreasing

From the table:

What are the y values doing as the x
values increase? If the y values increase, it is an increasing
equation. If the y values decrease, it is a decreasing equation.

increasing | decreasing | |||

x | y | x | y | |

-1 | -2 | 0 | 0 | |

0 | 0 | 1 | -2 | |

1 | 2 | 2 | -4 | |

2 | 4 | 3 | -6 | |

3 | 6 | 4 | -8 |

From the graph:

Check the direction of the graph
reading left to right. If the graph is moving up, it is increasing.
If the graph is moving sown, it is decreasing.

From the equation:

The sign of the coefficient is your
clue. If it is a positive number, it is increasing. If it is a
negative number, it is decreasing.

How to find the y-intercept

From the table:

The y-intercept is found where x is
zero. It is the corresponding y value.

y-intercept is (0, 0) | y-intercept is (0, 5) | |||

x | y | x | y | |

-1 | -2 | -1 | 4 | |

0 | 0 | 0 | 5 | |

1 | 2 | 1 | 6 | |

2 | 4 | 2 | 7 | |

3 | 6 | 3 | 8 |

From the graph:

Find the coordinate point where the
graph crosses the y axis

From the equation:

If the equation is in the form y = mx
+ b then the y-intercept is b

How to find the slope

From the table:

Write a ratio comparing a change in y
values to its corresponding change in x values. That ratio will give you
the slope.

y = 2x change is 2/1 | y = -x + 3 change is -2/2 | |||

x | y | x | y | |

0 | 0 | 0 | 3 | |

1 | 2 | 2 | 1 | |

2 | 4 | 4 | -1 | |

3 | 6 | 6 | -3 | |

4 | 8 | 8 | -5 |

From the graph:

Choose two points on the graph.
Reading left to right, count how the y changes compared to how the x changes.

From the equation:

The coefficient of x is your slope as
it is the rate of change in the equation.