Interpreting Linear Functions

Front

What does the slope represent in a linear function?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable. For example, if a sloth runs 6 feet in 1 minute, the slope is 6 feet/minute.

Front

What is glossophobia?

Back

Glossophobia is the fear of public speaking.

Front

What is a y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of the dependent variable when the independent variable is zero. For example, buying $30 worth of supplies for a lemonade stand can represent a y-intercept.

Front

How do you calculate the rate of change?

Back

The rate of change is calculated by dividing the change in the dependent variable by the change in the independent variable. For example, if rain falls 2 cm in 1 hour, the rate of change is 2 cm/hour.

Front

What does a greater rate of change indicate?

Back

A greater rate of change indicates that the dependent variable is changing more rapidly with respect to the independent variable. For example, if Water's Edge Rafts has a higher rate of change than Ryan's Rafts, it means Water's Edge Rafts is growing or changing faster.

Front

What is a linear function?

Back

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

Front

What does the term 'slope' mean in mathematics?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over change in x).

Front

What is the formula for calculating slope?

Back

The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the significance of the y-intercept in real-life situations?

Back

The y-intercept can represent initial conditions or starting values in real-life situations, such as initial investment or starting temperature.

Front

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

Back

In a real-world context, the slope can represent speed, growth rate, or any other rate of change, such as a car traveling at 60 miles per hour.