Determining Rate of Change and Initial Value

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which represents the amount of change in the dependent variable (y) for a unit change in the independent variable (x).

Front

How do you determine the initial value in a linear function?

Back

The initial value in a linear function is the y-intercept, which is the value of y when x is 0. It can be found in the equation of the line in the form y = mx + b, where b is the initial value.

Front

What is the slope of the function y = 2x + 2?

Back

The slope of the function y = 2x + 2 is 2.

Front

How do you calculate the total cost of a service that includes a flat fee and a variable charge?

Back

To calculate the total cost, use the equation y = mx + b, where m is the variable charge per unit (hour, ride, etc.), x is the number of units, and b is the flat fee.

Front

What is the equation for a linear function that has a slope of 26 and a y-intercept of 50?

Back

The equation for the linear function is y = 26x + 50.

Front

If a gym charges a one-time membership fee and a monthly fee, how can you express the total cost?

Back

The total cost can be expressed as y = mx + b, where m is the monthly fee, x is the number of months, and b is the one-time membership fee.

Front

What does the slope represent in a cost function?

Back

The slope represents the rate at which the cost increases with each additional unit of service (e.g., hour of work, ride, month).

Front

How can you find the cost per month if given total costs for different time periods?

Back

To find the cost per month, calculate the difference in total costs and divide by the difference in months.

Front

What is the y-intercept of the function y = -3x - 2?

Back

The y-intercept of the function y = -3x - 2 is -2.

Front

How do you interpret the slope of $1.50 in the context of a fair's ride cost?

Back

The slope of $1.50 indicates that for each additional ride taken, the total cost increases by $1.50.