Slope

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 the ratio of the vertical change to the horizontal change between two points on the line.

Tags

CCSS.8.EE.B.5

Front

How is slope calculated between two points (x1, y1) and (x2, y2)?

Back

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 vertical change regardless of the horizontal change.

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 is 0, leading to division by zero.

Tags

CCSS.8.EE.B.5

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you determine the slope from a linear equation in standard form?

Back

From the standard form Ax + By = C, the slope can be determined by rearranging the equation into slope-intercept form (y = mx + b) and identifying m.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does the term 'rate of change' refer to in the context of slope?

Back

The term 'rate of change' refers to how much the dependent variable (y) changes for a unit change in the independent variable (x), which is represented by the slope.

Tags

CCSS.8.EE.B.5