The number in front, and the lean

Draw y = x, y = 2x and y = 3x. What does the number in front do?

The rule

The number in front of x tells the lean of the line. The lean is how steep it is, up or down. For example, y = 3x is steeper than y = x.

In y = ax + b, the number a is the slope. It is the change in y for one step in x. One step means x goes up by 1.

• y = 2x + 6 rises 2 for each step. The slope is 2.
• y = 5x + 6 rises 5 for each step. That line is steeper than y = 2x + 6.
• y = 12 − 2x falls 2 for each step. The slope is −2.

For y = 12 − 2x, write y = −2x + 12. The number in front of x is −2.

Rise is the change in y. Run is the change in x. Take any two points on the line. Rise ÷ run gives the same slope for every pair.

A positive slope means growth: the output rises. A negative slope means decay: the output falls.

Try the lab to finish this lesson.