Linear vs Nonlinear Graphs

Front

What is a linear graph?

Back

A linear graph is a graph that represents a linear relationship between two variables, where the change in one variable is constant with respect to the other, resulting in a straight line.

Front

What is a nonlinear graph?

Back

A nonlinear graph is a graph that represents a nonlinear relationship between two variables, where the change in one variable is not constant with respect to the other, resulting in a curve or a line that is not straight.

Front

Give an example of a linear relationship.

Back

An example of a linear relationship is a worker getting paid $10 for every hour worked; the total pay increases linearly with hours worked.

Front

Give an example of a nonlinear relationship.

Back

An example of a nonlinear relationship is the path of a thrown ball, which follows a curved trajectory due to the effects of gravity.

Front

What does it mean if a graph is curved?

Back

If a graph is curved, it indicates a nonlinear relationship, meaning the rate of change between the variables is not constant.

Front

How can you identify a linear graph visually?

Back

A linear graph can be identified visually by its straight line, which can be ascending or descending but does not curve.

Front

What is the slope of a linear graph?

Back

The slope of a linear graph is the ratio of the vertical change to the horizontal change between any two points on the line.

Front

What does a vertical line represent in a graph?

Back

A vertical line in a graph represents an undefined slope and indicates a relationship where one variable does not change regardless of the other variable.

Front

What is the equation of a linear function?

Back

The equation of a linear function is typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a linear graph?

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of the dependent variable when the independent variable is zero.