2.2 Slope from TWO POINTS

Front

What is the slope formula used to calculate the slope between two points?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does it mean if the slope of a line is undefined?

Back

An undefined slope occurs when the line is vertical, meaning the x-coordinates of the two points are the same (e.g., (5, -10) and (5, -4)).

Front

How do you set up the slope calculation for points (6, 2) and (-8, 12)?

Back

The setup is: m = (12 - 2) / (-8 - 6) = 10 / -14 = -5/7.

Front

What is the slope between the points (-2, -5) and (-9, 0)?

Back

The slope is calculated as: m = (0 + 5) / (-9 + 2) = 5 / -7 = -5/7.

Front

How do you find the slope of a line that passes through the points (4, -7) and (6, -2)?

Back

The slope is calculated as: m = (-2 + 7) / (6 - 4) = 5 / 2.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

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-coordinates change.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope; they never intersect and maintain a constant distance apart.

Front

What is the relationship between slope and perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other; if one slope is m, the other is -1/m.

Front

How can you determine if two points form a vertical line?

Back

Two points form a vertical line if their x-coordinates are the same, resulting in an undefined slope.