Slope from a Graph

Front

What is the definition of slope in mathematics?

Back

Slope is the measure of the steepness or incline of a line, defined 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 of a line given 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

If a line has a slope of 1/3, what does this mean in terms of rise and run?

Back

A slope of 1/3 means that for every 3 units of horizontal change (run), there is a 1 unit of vertical change (rise).

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line that rises 4 units for every 1 unit it runs?

Back

The slope of the line is 4, calculated as rise/run = 4/1.

Tags

CCSS.8.EE.B.5

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the slope formula: m = rise/run.

Tags

CCSS.8.EE.B.5

Front

What is the relationship between slope and linear equations?

Back

In a linear equation of the form y = mx + b, 'm' represents the slope of the line, indicating its steepness and direction.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3