Slope from Graphs

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (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 x increases, y 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 x increases, y decreases, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where x remains constant, indicating that there is no change in x as y changes.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where b is the y-intercept.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where a is the x-intercept.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

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

Front

If a line has a slope of -3, what does this tell you about the line?

Back

A slope of -3 indicates that for every 1 unit increase in x, y decreases by 3 units.