Finding the Slope

Front

What is the definition of slope in mathematics?

Back

The 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

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 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

How can you find the slope from the equation of a line in slope-intercept form (y = mx + b)?

Back

In the slope-intercept form, 'm' represents the slope of the line.

Front

What is the slope of the line represented by the equation y = 2/3x - 6?

Back

The slope of the line is 2/3.

Front

What is the relationship between slope and rate of change?

Back

Slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What does the term 'rate of change' refer to in the context of a graph?

Back

Rate of change refers to how much the dependent variable changes for a given change in the independent variable, often represented by the slope.