Slope Basics Flashcard

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

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

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

In the slope-intercept form, what does the 'b' represent?

Back

In the slope-intercept form, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope, meaning they rise and fall at the same rate and will never intersect.

Front

What is the relationship between slope and perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one slope is m, the other is -1/m.