Slope and Similar 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 between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

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 a line has a slope of 3/4, what does this indicate about its steepness?

Back

A slope of 3/4 indicates that for every 4 units moved horizontally, the line rises 3 units vertically, making it moderately steep.

Front

What is the slope of line A if it rises 2 units for every 1 unit it runs?

Back

The slope of line A is 2.

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 the line rises 1 unit for every 1 unit it runs, creating a 45-degree angle with the horizontal.

Front

What is the relationship between similar triangles and slope?

Back

Similar triangles have the same shape but may differ in size; their corresponding sides are proportional, which means they have the same slope.

Front

If two lines are parallel, what can be said about their slopes?

Back

If two lines are parallel, they have the same slope.

Front

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

Back

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