Write linear functions: word problems

Learning Objectives Identify independent and dependent variables in a word problem. Determine the rate of change (slope) from a word problem. Identify the initial value (y-intercept) from a word problem. Write a linear function in slope-intercept form ($y = mx + b$) from a word problem. Interpret the meaning of the slope and y-intercept in the context of a word problem. Use a linear function to make predictions or solve related questions. Ever wonder how businesses predict costs or how much gas you'll use on a trip? ⛽️ It all starts with understanding how things change! In this lesson, you'll learn how to translate real-world scenarios into mathematical equations called linear functions. This skill helps you model situations, make predictions, and solve problems...

TermDefinitionExample Linear FunctionA relationship where a constant change in one quantity produces a constant change in another quantity. Its graph is a straight line.The total cost of renting a bike is $5 plus $2 per hour. This is a linear relationship. Independent VariableThe quantity that changes freely or causes another quantity to change. It's usually represented by 'x' and plotted on the horizontal axis.In the bike rental example, the number of hours (h) is the independent variable because the cost depends on the hours. Dependent VariableThe quantity whose value depends on the independent variable. It's usually represented by 'y' or $f(x)$ and plotted on the vertical axis.In the bike rental example, the total cost (C) is the dependent variable because...

Slope-Intercept Form of a Linear Function $y = mx + b$ This is the most common form for writing linear functions from word problems. 'm' represents the slope (rate of change), and 'b' represents the y-intercept (initial value or starting amount). Slope Formula (Rate of Change) $m = \frac{y_2 - y_1}{x_2 - x_1}$ Used to calculate the rate of change (slope) when two specific points $(x_1, y_1)$ and $(x_2, y_2)$ are given or can be derived from a word problem.