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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a linear function represent?

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0, representing the starting point of the function on the y-axis.

Front

How can you determine if a table of values represents a linear function?

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the function is linear.

Tags

CCSS.HSF-LE.A.1B

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the standard form of a linear equation?

Back

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

Front

If a linear function has a slope of 0, what does that indicate about the graph?

Back

A slope of 0 indicates that the graph is a horizontal line, meaning the y-value does not change as x changes.

Tags

CCSS.8.EE.B.5

Front

What is the difference between a linear and a nonlinear function?

Back

A linear function graphs to a straight line, while a nonlinear function graphs to a curve.

Tags

CCSS.8.F.A.3

Front

Write the linear function for a scenario where a person earns $15 per hour and has a starting salary of $200.

Back

The function can be written as E(x) = 15x + 200, where E is the earnings after x hours.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How do you find the cost function for a service that charges a flat fee plus a variable rate?

Back

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

Tags

CCSS.HSF.LE.B.5