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 line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

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 y = mx + b.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value). If any x-value is paired with more than one y-value, it is not a function.

Front

What is the equation of a line with a slope of 2/3 and a y-intercept of -3?

Back

y = (2/3)x - 3.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once. This is known as the vertical line test.

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

How can you find 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 the coordinates of the two points.

Front

What is the slope of the line represented by the equation y = -1x + 2?

Back

The slope of the line is -1.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant from left to right.