November 29th Flashcardziz: Recognizing Slope on Graphs

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 (rise) to the horizontal change (run) between two points on the line.

Front

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

Back

Slope (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 does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, where there is no change in the y-value as the x-value changes.

Front

What does it mean if a slope is undefined?

Back

An undefined slope occurs in a vertical line, where the x-value remains constant while the y-value changes, leading to division by zero.

Front

If a line has a slope of +5/3, how would you describe its steepness?

Back

The line is relatively steep, rising 5 units vertically for every 3 units it moves horizontally.

Front

If a line has a slope of -5/3, how would you describe its steepness?

Back

The line is relatively steep, falling 5 units vertically for every 3 units it moves horizontally.

Front

What is the slope of a line that is perfectly horizontal?

Back

The slope of a perfectly horizontal line is 0.

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.