Linear Functions (Day 5)

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It 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 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 in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

Write the equation of a linear function given a slope of 2 and a y-intercept of 3.

Back

The equation is y = 2x + 3.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

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

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 mean?

Back

A slope of 0 means the line is horizontal, indicating that y does not change as x changes.

Front

What is the significance of the x-intercept?

Back

The x-intercept is the point where the line crosses the x-axis. It is the value of x when y = 0.

Front

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

Back

A function is linear if the differences between consecutive y-values are constant for equal differences in x-values.

Front

What does it mean for a linear function to have a positive slope?

Back

A positive slope means that as x increases, y also increases, indicating a direct relationship.