Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope of a linear function from its equation?

Back

The slope of a linear function in the form y = mx + b is represented by the coefficient m. It indicates the rate of change of y with respect to x.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How can you compare the costs of two services represented by linear functions?

Back

To compare costs, evaluate both functions at the same input value (e.g., number of movies) and compare the resulting outputs.

Front

What is the significance of the slope in real-world applications?

Back

The slope indicates how much one quantity changes in relation to another, which can represent rates such as speed, cost per item, or growth rates.

Front

How do you find the y-intercept from a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What does it mean if one linear function has a higher slope than another?

Back

A higher slope means that the function increases at a faster rate compared to the other function.

Front

How can you determine which linear function has a higher y-intercept?

Back

Compare the constant term (b) in the equations of the linear functions; the function with the larger b value has a higher y-intercept.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

How do you interpret the slope in the context of a problem?

Back

The slope represents the rate of change between the two variables involved in the problem, providing insight into their relationship.