Slope from a line

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 ratio of the vertical change (rise) to the horizontal change (run) 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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-coordinate changes.

Front

What is the slope of a vertical line?

Back

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

Front

If a line has a slope of 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit of horizontal change (run), the vertical change (rise) is 2 units.

Front

How can you determine the slope from a linear equation in the form y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

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

Back

The slope of the line is -3.

Front

What is the slope of the line represented by the equation y = rac{1}{2}x - 1?

Back

The slope of the line is rac{1}{2}.