Interpreting Graphs of Linear Functions in Context

Front

What is the rate of change in a linear function?

Back

The rate of change represents how much the dependent variable (y) changes for a unit change in the independent variable (x). It is often represented by the slope of the line.

Front

What does the y-intercept represent in a graph?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the function on the y-axis.

Front

How do you interpret the slope of a line in a real-world context?

Back

The slope indicates the rate at which one quantity changes in relation to another. For example, a slope of 2 means that for every 1 unit increase in x, y increases by 2 units.

Front

What does it mean when a graph is increasing?

Back

An increasing graph indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does it mean when a graph is decreasing?

Back

A decreasing graph indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, which can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, calculate the change in y (rise) and the change in x (run), and then divide rise by run.

Front

What does a slope of 0 indicate?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, meaning x does not change while y changes.

Front

How do you determine the x-intercept from a graph?

Back

The x-intercept is the point where the graph crosses the x-axis, which occurs when y = 0.