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Math · Linear Functions

SAT linear functions: rate and starting amount

The rule

In y = mx + b, m is the change in y for each one-unit increase in x; b is the value of y when x = 0. Include the units.

(0, 4)(6, 19)Miles
A line passes through (0 miles, 4 dollars) and (6 miles, 19 dollars). The starting amount is 4 dollars; the increase is 2.50 dollars per mile.

Worked example

A ride costs $4 plus $2.50 per mile. How many miles does a $19 ride cover?

  1. Write the model: cost = 2.50 × miles + 4.
  2. Remove the starting fee: 19 − 4 = 15.
  3. Divide by the per-mile rate: 15 ÷ 2.50 = 6 miles. Check: 2.50 × 6 + 4 = 19.

A common trap

19 ÷ 2.50 ignores the fixed $4 fee. The graph starts at (0, 4), not at the origin.

Apply it, then revisit it

Try the skill in a separate question. After checking your answer, explain the step you used and return to any mistake later.

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