Interpret the graph of a linear function: word problems

Learning Objectives Identify the independent and dependent variables from a word problem and their representation on a graph. Determine the meaning of the x-intercept and y-intercept in the context of a word problem. Calculate and interpret the slope of a linear function from its graph in a real-world scenario. Use the graph of a linear function to answer specific questions related to a word problem. Predict future outcomes or past conditions by extending the graph of a linear function. Distinguish between reasonable and unreasonable interpretations of a graph based on the problem's context. Ever wonder how scientists predict weather patterns or how businesses track their profits? 📈 Graphs of linear functions help us understand these real-world situations by showing re...

TermDefinitionExample Linear FunctionA function whose graph is a straight line. It represents a constant rate of change between two variables.The relationship between the number of hours worked and the money earned at a constant hourly wage. Graph of a Linear FunctionA visual representation of a linear function on a coordinate plane, showing the relationship between two variables as a straight line.A line on a graph where the x-axis represents time and the y-axis represents distance, showing how far someone traveled over time. Independent Variable (x-axis)The variable that changes independently; its value determines the value of the dependent variable. It is typically plotted on the horizontal (x) axis.In a problem about distance traveled over time, 'time' is the independent var...

Slope Formula $m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$ This formula is used to calculate the rate of change (slope) between any two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ on a linear graph. In word problems, the slope tells you how much the dependent variable changes for every unit change in the independent variable, including its direction (increasing or decreasing). Equation of a Line (Slope-Intercept Form) $y = mx + b$ This equation describes any linear function, where $m$ is the slope and $b$ is the y-intercept. It helps relate the independent variable ($x$) to the dependent variable ($y$) and is useful for interpreting the starting point and constant rate of change in a real-world context. Interpreting Intercepts in Context Y-inter...