Slope from a Graph

Front

What is the definition of slope in a graph?

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.

Front

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

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates that the line is horizontal, meaning it does not rise or fall.

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 4/1, which simplifies to 4.

Front

What is the slope of a line that falls 1 unit for every 5 units it runs?

Back

The slope of the line is -1/5.

Front

What is the relationship between the slope of a line and its angle of inclination?

Back

The slope of a line is equal to the tangent of the angle of inclination with respect to the horizontal axis.

Front

How can you determine if a slope is positive, negative, or zero?

Back

A positive slope rises from left to right, a negative slope falls from left to right, and a zero slope is horizontal.

Front

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

Back

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

Front

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

Back

'Rise' refers to the vertical change between two points on a line.