Interpret the graph of a linear function: word problems

Learning Objectives Identify the independent and dependent variables from a linear graph in a word problem context. Interpret the real-world meaning of any given point (x, y) on a linear function graph. Calculate the slope of a linear graph and explain its meaning as a rate of change in a word problem. Identify the y-intercept of a linear graph and explain its meaning as an initial value or starting point. Use a linear graph to answer specific questions and make predictions related to a real-world scenario. Explain the real-world meaning of the x-intercept (if applicable) in a given context. Translate information from a word problem into a graphical representation and vice versa. Ever wonder how a simple line on a graph can tell a whole story about how much money you save...

TermDefinitionExample Linear FunctionA function whose graph is a straight line. It represents a relationship where there is a constant rate of change between two quantities.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, typically showing how one quantity (dependent variable) changes in relation to another (independent variable).A line on a graph where the x-axis is 'Time (hours)' and the y-axis is 'Distance (miles)'. Independent Variable (x-axis)The variable that changes independently and is typically plotted on the horizontal (x) axis. Its value determines the value of the dependent variable.In a graph showing distance vs....

Slope Formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Use this formula to calculate the slope (m) of a linear function given any two points $(x_1, y_1)$ and $(x_2, y_2)$ on the line. The slope represents the rate of change. Slope-Intercept Form $$y = mx + b$$ This equation represents a linear function where 'm' is the slope and 'b' is the y-intercept. It's useful for understanding the initial value and rate of change directly from the equation. Interpreting a Point (x, y) A point $(x, y)$ on a graph means 'When the independent variable is $x$, the dependent variable is $y$.' To understand the real-world meaning of any point on a linear graph, identify what the x-axis and y-axis represent, then state the values in context.