Types of Slopes

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 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

How can you identify a slope from a table of values?

Back

To identify the slope from a table, calculate the change in y (vertical change) divided by the change in x (horizontal change) between two points.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in the equation y - 4 = 2/3(x - 3)?

Back

In the equation y - 4 = 2/3(x - 3), the slope is 2/3, indicating that for every 3 units moved horizontally, the line moves up 2 units.

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 does the steepness of a slope affect the angle of a line?

Back

The steeper the slope, the larger the angle the line makes with the horizontal axis.

Front

What is the relationship between slope and rate of change?

Back

Slope represents the rate of change between two variables; a steeper slope indicates a greater rate of change.