Interpreting Graphs of Linear Functions in Context

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of y when x is 0.

Front

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

Back

The slope can be interpreted as the rate of change in a real-world scenario, such as speed, cost per item, or growth rate.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

What is the significance of the x-intercept in a graph?

Back

The x-intercept is the point where the graph crosses the x-axis, representing the value of x when y is 0.

Front

How can you determine the rate of change from a graph?

Back

The rate of change can be determined by calculating the slope of the line, which is the rise over run (change in y over change in x).

Front

What does the equation f(x) = mx + b represent?

Back

This equation represents a linear function where m is the slope and b is the y-intercept.

Front

What is the meaning of f(1990)=214 in a real-world context?

Back

It means that in the year 1990, the value of the function (e.g., population, sales) was 214.