Slopey Slope

Front

What is the definition of slope in mathematics?

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.

Tags

CCSS.8.EE.B.5

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (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 vertical change (rise) regardless of the horizontal change (run).

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 horizontal change (run) is 0, leading to division by zero.

Tags

CCSS.8.EE.B.5

Front

Find the slope of the line that passes through the points (1, 2) and (3, 6).

Back

Slope = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Tags

CCSS.8.EE.B.5

Front

Find the slope of the line that passes through the points (2, 3) and (5, 7).

Back

Slope = (7 - 3) / (5 - 2) = 4 / 3.

Tags

CCSS.8.EE.B.5

Front

If a line has a slope of -3, what does this tell you about the line's direction?

Back

A slope of -3 indicates that the line falls steeply from left to right.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope is 2, which means for every 1 unit increase in x, y increases by 2 units.

Tags

CCSS.8.EE.B.5