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 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The 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 a zero slope?

Back

A zero slope indicates a horizontal line where there is no change in y as x changes; the line remains constant.

Front

What is an undefined slope?

Back

An undefined slope occurs with a vertical line where there is no change in x; the slope cannot be calculated.

Front

If a line has a slope of 1/2, what does this mean?

Back

A slope of 1/2 means that for every 2 units moved horizontally (run), the line rises 1 unit vertically (rise).

Front

What is the slope of a line that goes through the points (2, 3) and (4, 7)?

Back

The slope is m = (7 - 3) / (4 - 2) = 4/2 = 2.

Front

If a line has a slope of -3, what does this indicate about its direction?

Back

A slope of -3 indicates that the line falls steeply from left to right, decreasing by 3 units in y for every 1 unit increase in x.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.