Equations of 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 (m) represent in a linear function?

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 the equation of a linear function?

Back

The y-intercept is the value of y when x is 0. It is represented by the term 'b' in the equation y = mx + b.

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line with a slope of 4 and a y-intercept of 16?

Back

The equation is y = 4x + 16.

Front

If a linear function has a slope of -2, what does this indicate about the line?

Back

A slope of -2 indicates that the line is decreasing; for every 1 unit increase in x, y decreases by 2 units.

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

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What does it mean if a linear function has a slope of 0?

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 slope in a real-world context?

Back

In real-world contexts, the slope can represent rates, such as speed, cost per item, or growth rates.