Writing Linear Functions from Tables
Writing linear functions from tables is a Grade 7 algebra skill in Big Ideas Math Advanced 2, Chapter 6: Functions. Students verify a constant rate of change, calculate slope using any two points with m equals (y2 minus y1) divided by (x2 minus x1), identify the y-intercept, and write the equation as y equals mx plus b. For example, points (0,3), (1,5), (2,7) give slope 2 and y-intercept 3, so the function is y equals 2x plus 3.
Key Concepts
To find a linear function from a table: (1) verify the data shows constant rate of change, (2) calculate slope using any two points with $m = \frac{y 2 y 1}{x 2 x 1}$, (3) identify the y intercept when $x = 0$ or use point slope form, (4) write the function as $y = mx + b$.
Common Questions
How do you write a linear function from a table of values?
Verify the rate of change is constant, calculate slope using two points, identify the y-intercept (the y-value when x is 0 or solve for b using any point), then write y equals mx plus b.
How do you check if a table represents a linear function?
Calculate the rate of change between consecutive rows. If the y-value changes by the same amount for each unit change in x, the relationship is linear.
What if the table does not include the point where x equals 0?
Calculate the slope m from two table points, then substitute any table point into y equals mx plus b and solve for b (the y-intercept).
What textbook covers writing linear functions from tables in Grade 7?
Big Ideas Math Advanced 2, Chapter 6: Functions covers writing linear function equations from tables of values.