[A] Slope (12.19)

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How is slope calculated?

Back

Slope (m) is calculated using the formula: m = \frac{y_2 - y_1}{x_2 - x_1}, where (x_1, y_1) and (x_2, y_2) are two points on the line.

Front

What does a positive slope indicate?

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?

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 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 rises 4 units for every 2 units it runs, what is the slope?

Back

The slope is \frac{4}{2} = 2.

Front

If a line falls 3 units for every 1 unit it runs, what is the slope?

Back

The slope is \frac{-3}{1} = -3.

Front

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

Back

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

Front

What is the slope of the line represented by the equation y = -5x + 1?

Back

The slope is -5, which is the coefficient of x in the equation.