Modeling and Interpreting 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 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 of 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 find the slope from a table of values?

Back

To find the slope from a table, calculate the change in y divided by the change in x (rise/run) between two points.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing a linear equation as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a linear function?

Back

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

Front

What does a negative slope indicate about a linear function?

Back

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

Front

How can you interpret the y-intercept in a real-world context?

Back

The y-intercept can represent the starting value of a situation before any changes occur.

Front

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

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they are parallel and will never intersect.