Distance and Slope

Front

What is the formula for calculating the slope of a line 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 x increases, y 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 x increases, y decreases, meaning the line falls from left to right.

Front

What is the distance formula used to calculate the distance between two points (x1, y1) and (x2, y2)?

Back

Distance = √((x2 - x1)² + (y2 - y1)²)

Front

Calculate the slope of the line between the points (2, 3) and (4, 7).

Back

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

Front

Calculate the distance between the points (1, 2) and (4, 6).

Back

Distance = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If the slope of a line is -3, what does this tell you about the line's direction?

Back

The line falls from left to right.

Front

What is the distance between the points (0, 0) and (3, 4)?

Back

Distance = √((3 - 0)² + (4 - 0)²) = √(9 + 16) = √25 = 5.