Slope of a Line

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. 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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero.

Front

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

Back

A slope of 2 means that for every 1 unit increase in x, y increases by 2 units.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope of the line is -3, which indicates a steep decline.

Front

How do you interpret a slope of 1/2?

Back

A slope of 1/2 means that for every 2 units you move to the right (increase in x), you move up 1 unit (increase in y).

Front

What is the slope of the line that passes through the points (1, 2) and (3, 4)?

Back

The slope is (4 - 2) / (3 - 1) = 2 / 2 = 1.