Slope and Similar Triangles

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, calculated 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 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.

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 3/2, what does this mean in terms of rise and run?

Back

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; their corresponding sides are proportional, which means they have the same slope.

Front

If triangle ABC has vertices A(1, 2), B(3, 6), and C(5, 4), what is the slope of line AC?

Back

Slope of AC = (4 - 2) / (5 - 1) = 2/4 = 1/2.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.