Slope from graphs, tables and points

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 from 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-values increase, the y-values also increase, 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-values increase, the y-values decrease, 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

In the context of a graph, what does the slope represent?

Back

In a graph, the slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Tags

CCSS.8.EE.B.5

Front

How can slope be interpreted in a real-world context?

Back

In real-world applications, slope can represent rates such as speed (distance over time), cost per unit (price over quantity), or productivity (output over input).

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line represented by the equation y = 3x + 2 is 3, which is the coefficient of x.

Tags

CCSS.8.EE.B.5

Front

How do you find the slope from a table of values?

Back

To find the slope from a table of values, select two points (x1, y1) and (x2, y2) from the table and use the slope formula: m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5