Rise over Run

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run).

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 zero, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because there is no horizontal change (run) while there is a vertical change (rise).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

If a line has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in the x-direction, the y-value increases by 2 units.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope of the line is -3.

Front

What is the slope of the line represented by the equation y = 1/2x - 1?

Back

The slope of the line is 1/2.

Front

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

The slope is (6 - 2) / (3 - 1) = 4 / 2 = 2.