Slope (Multiple Representations)

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

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

Back

Slope (m) is 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 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.

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.

Front

If a line has a slope of 1/2, what does this mean in terms of rise and run?

Back

A slope of 1/2 means that for every 2 units moved horizontally (run), the line rises 1 unit (rise).

Front

What is the slope of the line defined by the equation y = mx + b?

Back

The slope of the line is represented by 'm' in the equation y = mx + b.

Front

How can slope be represented in a table of values?

Back

Slope can be calculated by taking the difference in y-values divided by the difference in x-values between two points in the table.

Front

What is the slope of the line defined by y = 6.5x?

Back

The slope of the line is 6.5.