Identifying if Slope is Positive, Negative, Zero, or Undefin

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 the ratio of the vertical change to the horizontal change between two points on the line.

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 does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no vertical change as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where there is no horizontal change, making the slope calculation impossible.

Front

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

Back

You can determine the slope by observing the direction of the line: if it rises, it's positive; if it falls, it's negative; if it's horizontal, it's zero; if it's vertical, it's undefined.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

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

Front

If a line passes through the points (1, 5) and (1, 8), what is the slope?

Back

The slope is undefined because the x-values are the same, indicating a vertical line.

Front

If a line passes through the points (3, 2) and (3, 2), what is the slope?

Back

The slope is zero because there is no change in y as x changes; the points are the same.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.