Expressions, equations & relationships · TEKS 7.7
Linear relationships (y = mx + b)
A linear relationship changes by the same amount each step. Its equation is y = mx + b.
Key steps
- m = rate of change = change in y ÷ change in x.
- b = starting value (the y-value when x = 0).
- Word problems: "per hour/month/mile" is m; a one-time fee is b.
- If b = 0 the relationship is also proportional.
Worked example
A plumber charges $45 plus $30 per hour. Equation?
- Rate: $30 per hour, so m = 30. Starting fee: b = 45.
- Answer: y = 30x + 45
Watch out: Don’t swap them. The fee is paid once (b), while the hourly amount is multiplied by x (m).
Practice
5 questions with new numbers every set. Get 4 of 5 to mark this topic as practiced.