Slope from Two Points & Tables

Front

What is the formula to calculate the slope (m) 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 it mean if the slope of a line is positive?

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 it mean if the slope of a line is negative?

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 it mean if the slope is zero?

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 it mean if the slope is undefined?

Back

An undefined slope occurs when a line is vertical, meaning the x-coordinates are the same and there is no change in the x-coordinate.

Front

Find the slope of the line that passes through the points (1, -2) and (-2, 7).

Back

The slope is -3, calculated as m = (7 - (-2)) / (-2 - 1) = 9 / -3 = -3.

Front

Find the slope of the line that passes through the points (2, -1) and (2, -5).

Back

The slope is undefined because the x-coordinates are the same (2).

Front

What is the slope of the line that passes through the points (5, 0) and (0, 5)?

Back

The slope is -1, calculated as m = (5 - 0) / (0 - 5) = 5 / -5 = -1.

Front

If a line has a slope of 3/5, what does this indicate about the line's steepness?

Back

A slope of 3/5 indicates that for every 5 units moved horizontally to the right, the line rises 3 units vertically.

Front

How do you determine if two points create a vertical line?

Back

Two points create a vertical line if they have the same x-coordinate, resulting in an undefined slope.