Linear Functions

Front

What is the slope of the linear function represented by the equation y = 3/2x + 3?

Back

The slope is 3/2.

Front

What is the y-intercept of the linear function represented by the equation y = 3/2x + 3?

Back

The y-intercept is (0, 3).

Front

If a hot-air balloon rises at a constant rate and reaches 20 feet after 5 seconds, how can you express the relationship between time (x) and height (y)?

Back

The relationship can be expressed as a linear function, where y = mx + b, with m being the rate of rise.

Front

What does the slope represent in a real-world context, such as the height of a hot-air balloon over time?

Back

The slope represents the rate of change, or how much the height increases per unit of time.

Front

How do you determine the slope from a linear equation in the form y = mx + b?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the y-intercept in the equation y = -4x - 5?

Back

The y-intercept is -5.

Front

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

Back

The y-intercept represents the value of y when x is 0.

Front

How can you identify the slope from a graph of a linear function?

Back

The slope can be identified by calculating the rise over run between two points on the line.

Front

What is the significance of a negative slope in a linear function?

Back

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

Front

In the context of drilling an oil well, if the contractor drills 7 meters deeper every 2 hours, how can this be represented as a slope?

Back

The slope can be represented as 7 meters per 2 hours, or 3.5 meters per hour.