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 to the horizontal change 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 line that rises from left to right?

Back

The slope is positive.

Front

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

Back

The slope is negative.

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 1, what does this indicate about the angle of the line?

Back

A slope of 1 indicates that the line makes a 45-degree angle with the x-axis.

Front

What does a slope of -1 indicate about the line?

Back

A slope of -1 indicates that the line makes a 45-degree angle with the x-axis but falls from left to right.

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 their slopes are equal.

Front

If triangle ABC has a hypotenuse with a slope of -1/2, what does this tell you about the triangle's orientation?

Back

The hypotenuse slopes downward from left to right, indicating a negative slope.