Linear Function From a Context

1. Read the context carefully

A linear function from a context usually describes a situation that changes by a constant amount. Look for two pieces of information: a starting value and a rate of change. The starting value is the amount at the beginning, and the rate tells how much the quantity increases or decreases for each unit.

2. Build the equation

Use the form [ y = mx + b ] where:

• (m) is the rate of change,
• (b) is the starting value.

Match each part of the story to the correct number. If the context says “per hour,” “each ticket,” or “for every mile,” that is usually the slope. If it gives an initial fee, beginning amount, or value when (x=0), that is the intercept.

3. Write and simplify

Substitute the values into the formula and simplify the expression carefully. If the problem asks for a specific output, plug in the given input and compute the result step by step.

4. Check your answer

Make sure your equation fits the situation:

• Does it start at the correct initial value?
• Does it change by the right amount each time?
• If you substitute the given input, do you get a reasonable result?

A good check is to test the equation with the context’s numbers and confirm that the units and the trend make sense.