Rate of Change and Initial Value

Front

What is the definition of 'Rate of Change'?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often expressed as a ratio or a slope.

Front

What does 'Initial Value' refer to in a function?

Back

The initial value is the starting point of a function, often represented as the y-intercept in a linear equation.

Front

How can you determine if a function is linear?

Back

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

What is the slope of a line?

Back

The slope of a line is the ratio of the vertical change to the horizontal change between two points on the line.

Front

If a function has a slope of 2, what does this indicate?

Back

A slope of 2 indicates that for every 1 unit increase in the x-value, the y-value increases by 2 units.

Front

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

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a function?

Back

A positive slope indicates that the function is increasing; as the x-value increases, the y-value also increases.

Front

What does a negative slope indicate about a function?

Back

A negative slope indicates that the function is decreasing; as the x-value increases, the y-value decreases.

Front

In the context of a graph, what does the y-intercept represent?

Back

The y-intercept represents the initial value of the function, where the graph crosses the y-axis.

Front

How do you find the initial value from a table of values?

Back

The initial value is typically the y-value when the x-value is zero.