compare 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 f(x) = 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 of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

How do you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation f(x) = mx + b.

Front

If Function A has a slope of 3 and Function B has a slope of 2, which function is steeper?

Back

Function A is steeper because it has a greater slope (3 > 2).

Front

What does it mean if two linear functions are parallel?

Back

Two linear functions are parallel if they have the same slope but different y-intercepts. This means they will never intersect.

Front

What does it mean if two linear functions intersect?

Back

If two linear functions intersect, it means they have different slopes and will cross at a specific point, which represents a solution to the system of equations.

Front

How can you tell if a linear function is increasing or decreasing?

Back

A linear function is increasing if its slope is positive (m > 0) and decreasing if its slope is negative (m < 0).

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, and A should be non-negative.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x) has exactly one output (y). In a relation, an input can have multiple outputs.