Modeling and Interpreting Linear Functions

Front

What is the y-intercept in a linear function?

Back

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

Front

In the equation y = mx + b, what does 'm' represent?

Back

The slope of the line, which indicates the rate of change of y with respect to x.

Front

What does the slope of a linear function indicate?

Back

The slope indicates how much y changes for a unit change in x, representing the rate of change.

Front

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

Back

The y-intercept represents the starting value or initial condition of the situation being modeled.

Front

What is the general form of a linear equation?

Back

The general form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a candle burns at a rate of 2 cm per hour, what is the slope of the linear function representing its height over time?

Back

The slope is -2, indicating the height decreases by 2 cm for each hour.

Front

What does a positive slope indicate in a linear function?

Back

A positive slope indicates that as x increases, y also increases.

Front

What does a negative slope indicate in a linear function?

Back

A negative slope indicates that as x increases, y decreases.

Front

In the context of Taylor's earnings, what does the equation y = 200 + 5x represent?

Back

It represents that Taylor earns a base amount of $200 plus $5 for each person using her promo code.

Front

How can you find the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).