Finding the Slope of Lines

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the rise (vertical change) to the run (horizontal change).

Front

How do you calculate the slope of a line?

Back

Slope (m) = Rise / Run = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2).

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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no rise (vertical change) when moving along the line.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run (horizontal change) is 0, leading to division by zero.

Front

If a line rises 3 units and runs 4 units, what is the slope?

Back

Slope = Rise / Run = 3 / 4.

Front

If a line falls 2 units and runs 5 units, what is the slope?

Back

Slope = Rise / Run = -2 / 5.

Front

What is the slope of the line represented by the points (1, 2) and (4, 5)?

Back

Slope = (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

What is the slope of the line represented by the points (2, 3) and (2, 7)?

Back

The slope is undefined because the x-coordinates are the same (vertical line).