Types of Slopes

Front

What is the definition of a slope in mathematics?

Back

The slope is a measure of the steepness or incline of a line, represented as the ratio of the vertical change to the horizontal change between two points on the line.

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, resulting in an upward trend 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, resulting in a downward trend from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

How can you determine the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What type of slope does the equation y = mx + b represent when m > 0?

Back

When m > 0, the equation represents a positive slope.

Front

What type of slope does the equation y = mx + b represent when m < 0?

Back

When m < 0, the equation represents a negative slope.

Front

What is the significance of the y-intercept in the slope-intercept form of a line?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

What is the slope of the line represented by the equation y = 5?

Back

The slope of the line represented by the equation y = 5 is 0, as it is a horizontal line.