Finding slope using Slope triangles

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 slope triangles?

Back

To calculate the slope using slope triangles, identify two points on the line, create a right triangle where the vertical leg represents the change in y (∆y) and the horizontal leg represents the change in x (∆x). The slope (m) is then calculated as m = ∆y/∆x.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning there is no horizontal change as you move along the line.

Front

If ∆y = 6 and ∆x = 3, what is the slope of the line?

Back

The slope is 2/1.

Front

What is the slope of a line that rises 4 units for every 2 units it runs?

Back

The slope is 4/2, which simplifies to 2.

Front

What is the slope of a line that falls 3 units for every 5 units it runs?

Back

The slope is -3/5.

Front

If a line has a slope of 1, what does this mean about the angle of the line?

Back

A slope of 1 means that for every unit the line rises, it also runs one unit horizontally, creating a 45-degree angle with the x-axis.

Front

What is the formula for slope when given two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What is a slope triangle?

Back

A slope triangle is a right triangle formed by the rise and run of a line, used to visually represent and calculate the slope.