A.3(B) calculate the rate of change of a linear function

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 f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the rate of change represent in a linear function?

Back

The rate of change in a linear function represents how much the output (y) changes for a unit change in the input (x). It is equivalent to the slope (m) of the line.

Front

How do you calculate the slope of a linear function?

Back

The slope (m) of a linear function can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

Front

If a linear function has a slope of -2, what does this indicate about the function?

Back

A slope of -2 indicates that for every 1 unit increase in x, the value of y decreases by 2 units, showing a negative correlation.

Front

What is the y-intercept in the equation y = 4x - 5?

Back

The y-intercept is -5, which is the value of y when x = 0.

Front

How can you determine the rate of change from a graph of a linear function?

Back

To determine the rate of change from a graph, select two points on the line, find their coordinates, and use the slope formula m = (y2 - y1) / (x2 - x1).

Front

What is the significance of a slope of 0 in a linear function?

Back

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

Front

What does it mean if a linear function has a positive slope?

Back

A positive slope indicates that as the input (x) increases, the output (y) also increases, showing a direct relationship.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.