Slope and Similar Triangles

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually 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

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate 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 regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

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

Front

If a line has a slope of 3/2, what does this mean in terms of rise and run?

Back

A slope of 3/2 means that for every 2 units of horizontal change (run), the line rises 3 units (rise).

Front

What is the relationship between similar triangles and slope?

Back

Similar triangles have the same shape but may differ in size. The corresponding sides of similar triangles have the same ratio, which is equivalent to the slope of the line they lie on.

Front

How can you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the slope of a line that passes through the points (1, 2) and (4, 5)?

Back

The slope is calculated as m = (5 - 2) / (4 - 1) = 3/3 = 1.