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 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in y regardless of the change in x.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a vertical line?

Back

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

Tags

CCSS.8.EE.B.5

Front

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

Back

A slope of 3 means that for every 1 unit of horizontal change (run), the line rises 3 units (rise).

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 0.5x + 2?

Back

The slope of the line is 0.5, which is the coefficient of x in the slope-intercept form (y = mx + b).

Tags

CCSS.8.EE.B.5

Front

How can you determine if two triangles are similar using slopes?

Back

Two triangles are similar if their corresponding sides are proportional, which can be verified by comparing the slopes of their corresponding sides.

Tags

CCSS.8.EE.B.6

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.

Tags

CCSS.8.EE.B.5