Comparing Functions

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the constant value that represents the change in the dependent variable (y) for each unit change in the independent variable (x). It is often represented by the slope (m) in the equation y = mx + b.

Front

How can you determine if a graph is linear?

Back

A graph is linear if it forms a straight line when plotted on a coordinate plane. This means that the relationship between the x and y variables is consistent and can be described by a linear equation.

Front

What does the slope of a line indicate?

Back

The slope of a line indicates the steepness and direction of the line. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls. The absolute value of the slope indicates how steep the line is.

Front

How do you find the rate of change from a table of values?

Back

To find the rate of change from a table of values, calculate the difference in the y-values divided by the difference in the x-values for two points. This gives you the slope between those two points.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is zero and is denoted by the 'b' in the slope-intercept form of a linear equation (y = mx + b).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). In contrast, a relation can have multiple outputs for a single input.

Front

How can you compare the rates of change of two functions?

Back

To compare the rates of change of two functions, calculate the slope of each function. The function with the greater slope has a greater rate of change.

Front

What does it mean for a function to have a greater rate of change?

Back

A function with a greater rate of change increases or decreases more rapidly than another function. This is indicated by a steeper slope in its graph.

Front

How do you interpret the results of a linear function in a real-world context?

Back

Interpreting the results of a linear function in a real-world context involves understanding what the variables represent and how changes in one variable affect the other. For example, in a weight loss scenario, the slope may represent pounds lost per week.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) between two points is m = (y2 - y1) / (x2 - x1).