Grade 8 Math · Algebra

Linear patterns: tables, rate of change, and equations

Represent a linear growing or shrinking pattern with a table of values and an equation, find its rate of change and initial value, and use the equation to make predictions. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: G8-C1.1, G8-C1.2, G8-C1.3

Try one

Here is a table of values for a linear pattern: (0, 9), (1, 15), (2, 21), (3, 27). What is the rate of change?

Answer: 6

See one solved, step by step

Here is a table of values for a linear pattern: (2, 10), (3, 16), (4, 22), (5, 28). Using the rate of change, what is the initial value (the value when x = 0)?

📘 Worked solution
1Rate of change = 6 (y changes by this much every time x increases by 1).Subtract consecutive y-values to find the constant rate.
2From x = 2 back to x = 0 is 2 steps of size 6: 10 - 12 = −2.Undo the rate of change 2 times to work back to x = 0.
3Initial value = −2That's the value of y when x = 0.

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