Interpreting Graphs of Linear Functions in Context

Front

What does the slope represent in a linear function?

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the value of the dependent variable when the independent variable is zero.

Front

How do you calculate the slope from two points on a graph?

Back

Slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the meaning of a positive slope in a graph?

Back

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

Front

What does a negative slope indicate in 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, indicating where the dependent variable is zero.

Front

How can you interpret the steepness of a slope?

Back

The steeper the slope, the greater the rate of change; a flatter slope indicates a smaller rate of change.

Front

What does it mean if a graph is horizontal?

Back

A horizontal graph indicates that the dependent variable does not change as the independent variable changes (slope = 0).

Front

What is the formula for a linear function?

Back

The formula for a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The rate of change can be determined by calculating the slope between two points on the graph.