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 of a line 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 rise and the horizontal leg represents the run, and then use the formula: slope = rise/run.

Front

What does it mean for two triangles to be similar in the context of slope?

Back

Two triangles are similar if their corresponding angles are equal and their sides are in proportion, which means they have the same slope.

Front

If the slope of triangle ABC is 1, what is the slope of triangle DEF if they are similar?

Back

The slope of triangle DEF is also 1, as similar triangles have the same slope.

Front

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

Back

The slope of a line that goes down from left to right is negative.

Front

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

Back

The slope of a line that goes up from left to right is positive.

Front

How do you interpret a slope of 0?

Back

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

Front

What does an undefined slope represent?

Back

An undefined slope represents a vertical line, where there is no horizontal change.

Front

Calculate the slope of a line that passes through the points (2, 3) and (4, 7).

Back

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

Front

If a line has a slope of -5/4, what does this indicate about its steepness?

Back

A slope of -5/4 indicates that for every 4 units moved horizontally to the right, the line moves down 5 units, making it quite steep.