Linear functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by the value of b in the slope-intercept form 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 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 the domain and range of a function?

Back

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values).

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) is associated with exactly one output (y-value). This can be checked using the vertical line test on its graph.

Front

What does it mean for a linear function to be increasing or decreasing?

Back

A linear function is increasing if its slope is positive (m > 0), meaning as x increases, y also increases. It is decreasing if its slope is negative (m < 0), meaning as x increases, y decreases.

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 convert from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y: y = -A/B * x + C/B.