slope two points

Front

What is the slope of a line?

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 you move from left to right along the line, the line rises. This means that the y-values increase as the x-values increase.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as you move from left to right along the line, the line falls. This means that the y-values decrease as the x-values increase.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

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

Front

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

Back

A slope of 2 means that for every 1 unit you move horizontally to the right, the line rises 2 units vertically.

Front

Find the slope of the line that passes through the points (3, 4) and (7, 10).

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (10 - 4) / (7 - 3) = 6 / 4 = 1.5.

Front

What is the slope of the line that passes through the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

If the slope of a line is -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that as you move from left to right, the line falls steeply, decreasing by 3 units for every 1 unit you move to the right.