Finding Slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the change in the y-coordinate divided by the change in the x-coordinate between two points on the line.

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-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate 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 the y-coordinate as the x-coordinate changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning the x-coordinates are the same for two points, resulting in division by zero in the slope formula.

Front

Find the slope of the line through the points (2, 3) and (5, 11).

Back

m = (11 - 3) / (5 - 2) = 8 / 3.

Front

Find the slope of the line through the points (-1, 4) and (3, 4).

Back

m = (4 - 4) / (3 - (-1)) = 0 / 4 = 0.

Front

Find the slope of the line through the points (0, 0) and (0, 5).

Back

The slope is undefined because the x-coordinates are the same.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope is 2, which is the coefficient of x.