One input, one output

Put a number into 4x − 3. One number comes out. What comes out when x = 2?

The rule

At x = 2, 4x − 3 is 4 × 2 − 3 = 8 − 3 = 5.

A linear rule is y = ax + b, and a is not 0. Here x is the input and y is the output. The letters a and b are fixed numbers.

If a is 0, the rule is y = b. That is a constant. It never changes.

Multiply the input by a, then add b. The order is fixed.

An auto charges ₹30 to start and ₹12 for each kilometre. Let x be the kilometres and y the fare in rupees. The rule is y = 12x + 30.

• Multiply first: 12 × 3 = 36.
• Then add: 36 + 30 = 66. The fare is ₹66.
• Adding first is wrong: 3 + 30 = 33, then 12 × 33 = 396.

Put 2 in place of x to get the value at 2.

The rule accepts any number, even a negative one. Each input gives one output.