Writing a Function from a Table of Values
Grade 8 math students learn to write a linear function from a table of values by calculating slope and finding the y-intercept. First find slope using m = (y2-y1)/(x2-x1) between any two points, then identify or solve for b. If x=0 is not in the table, substitute slope and a point into y = mx + b to find b. Covered in Big Ideas Math, Course 3, Chapter 6: Functions.
Key Concepts
To write a linear function in the form $y = mx + b$ from a table of values, first find the slope ($m$) and then determine the y intercept ($b$).
1. Find the slope ($m$): Use any two points $(x 1, y 1)$ and $(x 2, y 2)$ from the table. $$m = \frac{{\text{change in } y}}{{\text{change in } x}} = \frac{{y 2 y 1}}{{x 2 x 1}}$$ 2. Find the y intercept ($b$): Identify the value of $y$ when $x=0$. If $x=0$ is not in the table, use the slope $m$ and any point $(x, y)$ from the table to solve for $b$ in the equation $y = mx + b$.
Common Questions
How do you write a function from a table of values?
Find the slope using m = (y2-y1)/(x2-x1) with any two points from the table. Then find the y-intercept: look for the y-value when x=0 or substitute the slope and a point into y = mx + b and solve for b.
How do you find slope from a table?
Choose any two rows from the table and use the slope formula m = change in y / change in x. For example, if one row is (1,6) and another is (2,8), slope = (8-6)/(2-1) = 2.
What if x=0 is not in the table?
If x=0 is not in the table, use the slope and any point from the table. Substitute both into y = mx + b and solve the equation for b, the y-intercept.
Which textbook covers writing functions from tables for Grade 8?
This topic is in Big Ideas Math, Course 3, Chapter 6: Functions.
What grade level covers writing functions from tables?
Writing functions from tables of values is typically covered in Grade 8 math.