Finding Slope

Front

What is the definition of slope in mathematics?

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 between two points (x1, y1) and (x2, y2)?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down and does not have a defined angle.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as you move along the line.

Front

Given the points (3, 4) and (3, 10), what is the slope?

Back

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

Front

If a line passes through the points (1, 2) and (4, 5), what is the slope?

Back

The slope is (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing an upward trend.

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, showing a downward trend.

Front

How do you interpret a slope of -6?

Back

A slope of -6 means that for every 1 unit increase in the x-direction, the y-value decreases by 6 units.

Front

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

Back

The slope of the line is 2, which indicates that for every 1 unit increase in x, y increases by 2 units.