Construct Linear Functions

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function represents how much the output (y) changes for a unit change in the input (x). It is often referred to as the slope.

Front

What is the initial value in a linear function?

Back

The initial value is the value of the function when the input (x) is zero. It is represented by the y-intercept in the equation y = mx + b.

Front

What does the slope of a linear function indicate?

Back

The slope indicates the steepness of the line and the direction of the relationship between x and y. A positive slope means y increases as x increases, while a negative slope means y decreases as x increases.

Front

How do you identify a function from a set of points?

Back

A set of points represents a function if each input (x-value) corresponds to exactly one output (y-value). If any x-value is repeated with different y-values, it is not a function.

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 slope-intercept form of a linear equation?

Back

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

Front

How do you find the slope from two points?

Back

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

Front

What is the y-intercept of the equation y = 3x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.

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 the output (y) does not change regardless of the input (x).

Front

What is the relationship between the slope and the rate of change?

Back

The slope of a linear function is the same as the rate of change. It quantifies how much y changes for a unit change in x.