Slope Intro

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 (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

The slope (m) can be 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 constant of proportionality in a linear relationship?

Back

The constant of proportionality is the slope of the line when the relationship is proportional, indicating the ratio of y to x remains constant.

Tags

CCSS.HSF-LE.A.1B

Front

What does it mean for a relationship to be linear but not proportional?

Back

A linear relationship is one that can be represented by a straight line, but if it is not proportional, it does not pass through the origin (0,0).

Tags

CCSS.8.F.A.3

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified from a graph if the line passes through the origin and has a constant slope.

Tags

CCSS.7.RP.A.2D

Front

What is the formula for the equation of a line in slope-intercept form?

Back

The slope-intercept form of a line is given by the equation: 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