Write a linear function from a table

Learning Objectives Identify linear relationships within a table of values. Accurately calculate the slope (rate of change) from any two points in a table. Determine the y-intercept of a linear function from a table. Write a linear function in slope-intercept form (y = mx + b) using data from a table. Verify the derived linear function using additional values from the table. Understand the meaning of the slope and y-intercept in the context of the table's data. Ever wonder how scientists predict future trends or how much a taxi ride will cost based on distance? 📈 It often starts with understanding patterns in data! In this lesson, you'll learn how to take a set of numbers organized in a table and turn it into a powerful mathematical rule called a linear function....

TermDefinitionExample Linear FunctionA function whose graph is a straight line, meaning it has a constant rate of change. It can be represented by an equation of the form y = mx + b.The relationship between hours worked (x) and money earned (y) at a constant hourly wage is a linear function. Table of ValuesAn organized list that shows the relationship between two variables, typically 'x' (input/independent variable) and 'y' (output/dependent variable).A table showing (1, 5), (2, 7), (3, 9) where x is the input and y is the output. Slope (Rate of Change)The measure of the steepness of a line, indicating how much the 'y' value changes for every unit change in the 'x' value. It's often described as 'rise over run'.If y increases by 2 eve...

Slope Formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Use this formula to calculate the slope (m) of a linear function when you have two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ from the table. The order of subtraction must be consistent for both x and y. Slope-Intercept Form of a Linear Equation $$y = mx + b$$ This is the standard form to write a linear function. Once you find the slope (m) and the y-intercept (b), substitute their values into this equation to represent the function. Finding the Y-intercept (b) $$b = y - mx$$ After calculating the slope (m), you can use any point (x, y) from the table and the slope-intercept form to solve for 'b'. Rearrange $y = mx + b$ to isolate 'b'.