Understanding Linear Relationships and Functions

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate between two points on the line. It is often represented as 'm' in the equation of a line.

Front

How do 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 means that no x-value can be repeated with a different y-value.

Front

What is the equation of a line that passes through the origin?

Back

The equation of a line that passes through the origin has the form y = mx, where m is the slope of the line.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is 0 in the equation of the line.

Front

What is the rate of change in a linear function?

Back

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

Front

How do you find the slope between 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 a function table?

Back

A function table is a table that shows the input values (x) and their corresponding output values (y) for a function. It helps visualize the relationship between the variables.

Front

What is the difference between a function and a relation?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.