Finding Slope from a Graph Flashcard

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

How do you calculate the slope from 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-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 a slope of zero mean?

Back

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

Front

What does an undefined slope mean?

Back

An undefined slope occurs with a vertical line, where the x-value does not change, leading to division by zero.

Front

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

Back

Slope = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line has a slope of -3, what does this tell you about the line?

Back

The line falls as it moves from left to right, indicating a negative relationship between x and y.

Front

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

Back

The slope of a perfectly vertical line is undefined.

Front

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

Back

The slope of a perfectly horizontal line is zero.