Interpreting Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you interpret the profit function y = 100,000 - 2,000x?

Back

In this function, the profit decreases by $2,000 for each month (x) that passes, starting from a maximum profit of $100,000.

Front

What is the equation for the total cost of a holiday meal for x people?

Back

The equation is y = 30 + 12.5x, where $30 is the delivery fee and $12.50 is the cost per person.

Front

How do you find the number of bottles left after x days if a family drinks 5 bottles per day?

Back

The equation is y = 48 - 5x, where 48 is the initial number of bottles and 5x represents the total bottles consumed after x days.

Front

What does the equation y = 10x + 40 represent in a gym membership scenario?

Back

This equation represents the total cost (y) of joining a gym, where $40 is the startup fee and $10 is the monthly fee for x months.

Front

How do you calculate the population after a certain number of years using the function y = 60,000 - 500x?

Back

To find the population after x years, substitute x into the equation. For example, after 9 years, y = 60,000 - 500(9) = 55,500.

Front

What is the significance of the negative sign in the equation y = 48 - 5x?

Back

The negative sign indicates a decrease in the number of bottles over time, as the family consumes 5 bottles each day.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.