Write a linear function from a table

Learning Objectives Identify independent and dependent variables in a table of values. Calculate the rate of change (slope) from a given table. Determine the y-intercept of a linear function from a table or by calculation. Write a linear function in slope-intercept form ($y = mx + b$) given a table of values. Verify if a given table represents a linear relationship. Use a derived linear function to predict values not explicitly shown in the table. Ever wonder how scientists predict future trends or how businesses forecast sales? 📈 It often starts with understanding patterns in data! In this lesson, you'll learn how to take a set of data presented in a table and turn it into a powerful mathematical rule called a linear function. This skill helps us describe relationshi...

TermDefinitionExample Linear FunctionA function whose graph is a straight line. It describes a relationship where the dependent variable changes at a constant rate with respect to the independent variable.The relationship between the number of hours you work and the total money you earn at a fixed hourly wage. Table of ValuesAn organized list that shows the relationship between two variables, typically an input (x) and an output (y).A table showing (hours worked, money earned): (1, $10), (2, $20), (3, $30). Independent Variable (x)The input variable whose value can be chosen freely or changes independently. It's usually represented on the horizontal axis.In a table of (time, distance), 'time' is the independent variable. Dependent Variable (y)The output variable whose value...

Slope Formula $m = \frac{\text{change in y}}{\text{change in x}} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ Use this formula to calculate the slope (m) of a linear function given any two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ from the table. It represents the constant rate of change. Slope-Intercept Form of a Linear Equation $y = mx + b$ Once you have found the slope (m) and the y-intercept (b), substitute these values into this form to write the complete linear function. This equation allows you to find any y-value for a given x-value.