Calculating Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

How is slope calculated?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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 zero slope indicate?

Back

A zero slope indicates a horizontal line, where there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-value remains constant while the y-value changes.

Front

How many graphs can have a positive slope?

Back

There can be multiple graphs with a positive slope, specifically 3 in the context of the provided questions.

Front

If the slope of a line is -5/3, what does this tell you about the line?

Back

A slope of -5/3 indicates that for every 3 units the line moves horizontally to the right, it moves 5 units down.

Front

What is the slope of a line represented by the equation y = 4x + 2?

Back

The slope of the line is 4, which means it rises 4 units for every 1 unit it moves to the right.

Front

What is the slope of a line represented by the equation y = -rac{1}{4}x + 3?

Back

The slope of the line is -rac{1}{4}, indicating it falls 1 unit for every 4 units it moves to the right.