Slope Triangles (24-25)

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented 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 using 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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

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

Front

How can slope triangles be used to find the slope of a line?

Back

Slope triangles are right triangles formed by the rise and run between two points on a line. The slope is calculated as the ratio of the length of the rise to the length of the run.

Front

If a slope triangle has a rise of 3 units and a run of 4 units, what is the slope?

Back

Slope = rise/run = 3/4.

Front

If a slope triangle has a rise of -2 units and a run of 5 units, what is the slope?

Back

Slope = rise/run = -2/5.

Front

What is the slope of a line that goes down from left to right?

Back

The slope is negative.