Modeling and Interpreting Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation 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 (m) represent in a linear function?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

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

Back

The y-intercept 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) based on the context, then formulate the equation in the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does it mean if the slope of a linear function is positive?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Tags

CCSS.8.EE.B.5

Front

What does it mean if the slope of a linear function is negative?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Tags

CCSS.8.EE.B.5

Front

In the equation y = 200 + 5x, what does the 200 represent?

Back

The 200 represents the initial value or fixed amount earned before any additional earnings from the variable part (5x) are added.

Tags

CCSS.HSF.LE.B.5

Front

In the equation y = 30 + 12.5x, what does the 12.5 represent?

Back

The 12.5 represents the cost per person for the holiday meal, indicating how much the total cost increases with each additional person.

Tags

CCSS.HSF.LE.B.5

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept often represents a starting point or initial condition in a real-world scenario, such as initial costs or starting quantities.

Tags

CCSS.HSF.LE.B.5

Front

How can you determine the slope from a graph?

Back

The slope can be determined by selecting two points on the line, calculating the rise (change in y) over the run (change in x) between those points.

Tags

CCSS.8.EE.B.5