Determining Slope from Graphs, Tables, and Two Points

Front

What is slope?

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 a line.

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).

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.

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.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating no change in the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, indicating that the x-value does not change while the y-value does.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).

Front

If a line passes through the points (1, 2) and (1, 5), what is the slope?

Back

The slope is undefined because the x-values are the same, indicating a vertical line.

Front

What is the slope of a line that rises 3 units for every 6 units it runs?

Back

The slope is 1/2, calculated as 3/6.

Front

How do you interpret a slope of -3?

Back

A slope of -3 indicates that for every 1 unit increase in x, the y-value decreases by 3 units.