Comparing Functions

Front

What is the equation to calculate the total charge for a service that includes a per hour rate and a fixed fee?

Back

y = mx + b, where m is the hourly rate and b is the fixed fee.

Front

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

Back

The slope is the coefficient of x, represented by m.

Front

What does a higher slope indicate in terms of rate of change?

Back

A higher slope indicates a greater rate of change, meaning the dependent variable changes more rapidly with respect to the independent variable.

Front

In the equations y = 3x - 1 and y = 1/2x + 1, how do you determine which has a higher y-intercept?

Back

The y-intercept is the constant term (b) in the equation. Compare the values of b in both equations.

Front

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

Back

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

Front

If a business charges a flat fee plus a variable rate, how can you express this as a linear equation?

Back

The equation can be expressed as y = mx + b, where m is the variable rate and b is the flat fee.

Front

What is the formula for calculating the total cost if a service has a fixed fee and a variable hourly charge?

Back

Total Cost = Fixed Fee + (Hourly Rate * Number of Hours) or y = b + mx.

Front

How can you compare the slopes of two linear equations to determine which has a greater rate of change?

Back

Compare the coefficients of x (m) in both equations; the larger coefficient indicates a steeper slope and greater rate of change.

Front

What does it mean if two lines are parallel in terms of their slopes?

Back

If two lines are parallel, they have the same slope (m) but different y-intercepts (b).

Front

How do you find the total cost for a service that charges a fixed fee and a variable fee based on usage?

Back

Add the fixed fee to the product of the variable fee and the quantity used.