Slope of a Line

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated 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

Slope (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 (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change (run) is 0, leading to division by zero.

Front

What is the constant rate of change in relation to slope?

Back

The constant rate of change is represented by the slope of the line, calculated as Rise/Run.

Front

If a line has a slope of 8, what does this mean?

Back

A slope of 8 means that for every 1 unit increase in x, the y-value increases by 8 units.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Front

How can you determine if a slope is positive, negative, zero, or undefined from a graph?

Back

A positive slope rises from left to right, a negative slope falls from left to right, a horizontal line has a slope of zero, and a vertical line has an undefined slope.