Slope Notes

What does slope describe in a graph?

The steepness and direction of a line.

How is slope calculated?

Slope is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points.

What does 'rise' represent in slope calculations?

The vertical distance between two points on a line.

What does 'run' represent in slope calculations?

The horizontal distance between two points on a line.

What does a positive rise indicate?

An upward slope.

What does a negative rise indicate?

A downward slope.

How is the slope (m) of a line defined mathematically?

m = (y2 - y1) / (x2 - x1) for points (x1, y1) and (x2, y2).

What does a larger absolute value of slope indicate?

A steeper line.

What does a positive slope signify when interpreting a line?

The line rises from left to right.

What does a negative slope signify when interpreting a line?

The line falls from left to right.

What does a slope of zero represent?

A horizontal line.

What does an undefined slope represent?

A vertical line.

Where is slope applied in real-world scenarios?

Calculating the grade of a road, determining the steepness of a roof, and analyzing rates of change.

Why is understanding slope important?

It helps in solving problems related to speed, distance, and time.

Summarize the concept of slope in mathematics.

Slope describes the steepness and direction of a line, calculated as rise over run, and interpretable for various real-world applications.