Slope & Comparing Rates of Change Review

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

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, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the slope of the line represented by the equation y = 5x + 2?

Back

The slope of the line is 5.

Front

If a line has a slope of 0, what does this mean?

Back

A slope of 0 means the line is horizontal and there is no change in y as x changes.

Front

If a line is vertical, what is its slope?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

What is the rate of change in a real-world context?

Back

The rate of change describes how one quantity changes in relation to another quantity, often represented by the slope of a graph.

Front

How can you compare the rates of change of two different linear equations?

Back

You can compare the slopes of the equations; the one with the greater absolute value of slope has a greater rate of change.

Front

What is the slope of the line that passes through the points (2, 3) and (4, 7)?

Back

The slope is (7 - 3) / (4 - 2) = 4 / 2 = 2.