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 of a linear function represent?

Back

The slope 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

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

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 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If a linear function has a slope of 0, what does that indicate?

Back

A slope of 0 indicates that the function is a horizontal line, meaning the output (y) does not change regardless of the input (x).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x) is associated with exactly one output (y).

Front

How can you determine if a set of points represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, 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 does the term 'initial value' refer to in a linear function?

Back

The initial value refers to the y-intercept of the function, which is the starting value of y when x is 0.