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

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. 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 write a linear function from a word problem?

Back

Identify the initial value and the rate of change. Use the form y = mx + b, where m is the rate of change and b is the initial value.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

y = 2x + 3

Front

If a linear function has a slope of -1, what does this indicate about the line?

Back

A slope of -1 indicates that the line decreases as x increases, meaning for every unit increase in x, y decreases by 1.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers unless specified otherwise by the context of the problem.

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers unless restricted by the context of the problem.

Front

How do you find the cost function for a service with a fixed fee and a variable rate?

Back

The cost function can be expressed as C(x) = fixed fee + (variable rate * x), where x is the number of units.

Front

What is the significance of the point (0, b) in a linear function?

Back

The point (0, b) represents the y-intercept of the linear function, indicating where the line crosses the y-axis.