Slope (from a graph)

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 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 zero slope indicate about a line?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, where there is no horizontal change as the x-value remains constant.

Front

If a line passes 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 1/2, what does this mean in terms of rise and run?

Back

For every 1 unit of vertical rise, there is a 2 unit horizontal run.

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.