Linear Equations ....................................

Quick Graphs
Here are three quick ways to plot the graph of a linear rule or equation.

Method 1: Find the Intercepts

This method is quick because the two points we're looking for have zeroes in them, so they're easy to solve for. Equations containing both variables x and y will result in an oblique line.

4x - 8y = 12

Finding the x intercept: let the y value be 0

4x - 8(0) = 12 and solve for x

4x = 12

x = 3

Since y = 0, the x intercept is (3, 0)

Finding the y intercept: let the x value be 0

4(0) - 8y = 12 and solve for y

-8y = 12

y = -1.5

Since x = 0, the y intercept is (0, -1.5)

Method 2: Horizontal or Vertical Lines

4x - 4 = 12

This equation has just x's, so it must be a vertical line.
Solve and graph:

4x - 4 = 12

4x = 16

x = 4
This is a vertical line at 4

2y + 7 = 12

This equation has just y's, so it's a horizontal line.
Solve and graph:

2y + 7 = 12

2y = 5

y = 2.5
This is a horizontal line at 2.5

Method 3: Slope-Y Intercept Method

Before we show you this method, there are some more facts about lines that you need to know. Learn about slopes and y intercepts here. Then come back.

If you know the equation of a line, and it's in 'y =' form, you can graph the line very quickly without making a table of points.

Let's look at the example y = 3x - 4

You've just learned that the slope of this line is 3, and the y intercept is (0, -4). That gives us a starting point, (0, -4). Locate that point on the graph.

The slope is 3. Make this into a fraction '3 over 1' so you have a 'rise over run'.

Start at (0, -4). Run 1 and rise 3. This will take you to another point on the line (1, -1).

Draw the line through (0, -4) and (1, -1), and there's your graph!

Here's another one: y = ¾ x - 2

The y intercept is (0, -2). Plot that first.

The slope is ¾, which is already a fraction.
Run is 4, rise is 3. Start at (0, -2) and run 4, rise 3

Now you're at (4, 1). Plot that.

Join (0, -2) and (4, 1)

Done!