Finding 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 does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change (run = 0), making the slope calculation impossible.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change (rise) as the x-values change.

Front

If the slope of a line is 3, what does this mean in terms of rise and run?

Back

A slope of 3 means that for every 1 unit of horizontal change (run), the line rises 3 units (rise).

Front

Find the slope of the line passing through the points (2, 3) and (5, 11).

Back

The slope is (11 - 3) / (5 - 2) = 8 / 3.

Front

Find the slope of the line passing through the points (-4, 5) and (-4, 2).

Back

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

Front

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

Back

The slope is 2, which is the coefficient of x in the equation.