Interpreting Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and 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 (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

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

Back

The y-intercept (b) is the value of y when x is 0; it represents the starting point of the function on the y-axis.

Front

How do you write the equation of a linear function from a word problem?

Back

Identify the fixed costs (y-intercept) and the variable costs (slope) from the problem, then use the form y = mx + b.

Front

If a gym charges a startup fee and a monthly fee, how do you model this with a linear equation?

Back

The equation is y = mx + b, where m is the monthly fee and b is the startup fee.

Front

What does d(4) = 37 mean in the context of Derek's earnings?

Back

It means that after working for 4 hours, Derek has earned a total of $37.

Front

How do you determine the number of items left after a certain period using a linear function?

Back

Use the equation y = initial amount - (rate of consumption * time) to find the remaining items.

Front

What is the function f(x) = 9x + 5 used for?

Back

It represents a linear relationship where for every x units, the output increases by 9 and starts at 5.

Front

How do you evaluate a function at a specific point, such as f(7)?

Back

Substitute the value of x into the function and calculate the result.

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 12.5 is the cost per person.