Calculating Slope

Front

What is the formula for calculating the slope of a line?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, 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-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What does an undefined slope indicate?

Back

An undefined slope occurs in vertical lines, where the change in x (denominator) is zero, making the slope calculation impossible.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no change in y as x changes.

Front

How do you determine if a slope is positive, negative, or undefined from a graph?

Back

A slope is positive if the line rises from left to right, negative if it falls from left to right, and undefined if the line is vertical.

Front

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

Back

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

Front

If a line has a slope of 0, what can be said about its equation?

Back

The equation of a line with a slope of 0 is of the form y = b, where b is the y-intercept.

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change, such as speed, cost per item, or growth rate, in various real-world contexts.

Front

How can you identify the slope from a linear equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, m represents the slope of the line.