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 (rise) to the horizontal change (run) between two points on the line.

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

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, 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-values increase, the y-values decrease, 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 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit of horizontal change (run), there is a 2 unit increase in vertical change (rise).

Front

What is the constant of proportionality in a proportional relationship?

Back

The constant of proportionality is the slope of the line that represents the relationship, indicating how much y changes for a unit change in x.

Front

Given the points (1, 2) and (3, 6), find the slope.

Back

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

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope is 3, which indicates that for every 1 unit increase in x, y increases by 3 units.