Slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented by the letter '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.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line has a slope of m = 1, what does this mean?

Back

A slope of m = 1 means that for every unit increase in x, y increases by the same amount, resulting in a 45-degree angle line.

Front

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

Back

The slope of the line is 3.

Front

Find the slope of the line passing through the points (2, 5) and (3, 6).

Back

The slope is m = 1.

Front

What is the slope of the line represented by the equation y = -rac{1}{2}x + 4?

Back

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