Slope (Multiple Representations)

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 is slope calculated using two points (x1, y1) and (x2, y2)?

Back

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-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 does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating no change in the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the x-value does not change, leading to division by zero in the slope formula.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

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

Back

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

Front

How can slope be represented in a table of values?

Back

Slope can be represented in a table by calculating the change in y-values divided by the change in x-values between two points.

Front

What is the slope of the line that passes through the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-values are the same, resulting in a vertical line.