Most of the lines you will be graphing will much more complex than simple vertical and horizontal lines. There are many ways to go about graphing these, but we will only work with the two most common methods: plotting points and slope-intercept form.

**Graphing lines by plotting points** is pretty simple. Just find two or more points - any (x,y) points - on the line and connect the dots.

Although you really only need two points to make a line, finding a third one is often a good idea. If all three points lie in a straight line, you can feel confident that you didn't make a mistake. If the third point doesn’t fit your line, check your work and try again.

Let's start with a simple example:

To find three points on this line, pick any values you want for one variable, plug them into the equation, then solve for the other variable.

Since y is already isolated in this equation, it would be a good idea to start by picking values for x. This will give you a value for x and one for y; an (x, y) point!

Here’s a tip: in the beginning, go easy on yourself and pick nice and simple values for x, like -1, 0, and 1.

**Pick an x value** | **Plug into y = 2x + 1** | **Solve for y** | **(x, y)** |

| |
| (0,1) |

1 | |
| (1,3) |

-1 | |
| (-1,1) |

Now that we have our three points, we can plot these on a coordinate grid and connect.

**Look Out:** although you can graph a line by only plotting two points, it is always a good idea to do at least three. If all three lie in a straight line, you can feel pretty confident that your answer is correct.

## Graphing Lines By Plotting Points Practice:

Graph the equation y = -½x – 2. | |

Again, it would probably be best to pick some values for x and solve for y, since y is already isolated. **x** | **y = -½x – 2** | **(x, y)** | | y = -½(0)– 2
y = 0 – 2
y = -2 | (0, -2) | 1 | y = -½(1)– 2
y = -½ – 2
y = -2½ | (1, -2½) | 2 | y = -½(2)– 2
y = -1 – 2
y = -3 | (2, -3) |
| |

Now let's plot them and connect them: | |

Graph the equation x + 3y = 7. | |

With all equations, it is really up you which variable to solve for, but for this problem it would be easiest to solve for x, since it doesn't have a coefficient. | | | *subtract 3y from each side* | | *simplify* |
| |

Now, let's plug in some numbers for y and solve for x. **y** | **x = 7 – 3y** | **(x, y)** | | x = 7 – 3(0)
x = 7 – 0
x = 7 | (7, 0) | 1 | x = 7 – 3(1)
x = 7 – 3
x = 4 | (4, 1) | 2 | x = 7 – 3(2)
x = 7 – 6
x = 1 | (1, 2) |
| |

Since we picked values for y and solved for x, we must be careful to plot them in the correct order, x then y. | |

Graph the equation 2y = 6x. | |

Let's solve this one for y. | | | *subtract 3y from each side* | | simplify |
| |

Now, let's plug in some numbers for x and solve for y. **x** | **y = 3x** | **(x, y)** | | y = 3(0)
y = 0 | (0, 0) | 1 | y = 3(1)
y = 3 | (1, 3) | -1 | y = 3(-1)
y = -3 | (-1, -3) |
| |

Plot and connect. | |

Graph the lines y = ½ and x = -½ on the same coordinate grid.

Hint

the first is horizontal and the 2nd is vertical

Answer

Graph the line: y = 4x – 3.

Hint

pick some values for x and solve for y

Answer

Graph the line: 5x + 10y = 25.

Hint

you might want to solve this one for x

Answer