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(-3, 0); slope = 2/3

(2, -2); slope = 1
(6, 2) and (-3, -7)
A) Which pair represents a line with a slope of 2/3?
B) Which point is on a line with a slope of 1?
C) Which pair represents a horizontal line?
D) Which pair represents a vertical line?

1 Answer

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Final answer:

The point (-3, 0) with a slope of 2/3 represents a line with that slope. The point (2, -2) lies on a line with a slope of 1. However, none of the given pairs represent horizontal or vertical lines as their coordinates do not satisfy the conditions for such lines.

Step-by-step explanation:

The question asks about the slope of lines represented by given points and slopes. To determine which pair of points represents a line with a specific slope, we can use the slope formula: slope (m) = (y2 - y1) / (x2 - x1). A line with a slope of 2/3 would rise 2 units for every 3 units it runs horizontally. A line with a slope of 1 rises 1 unit for every 1 unit it runs, thus forming a 45-degree angle with the x-axis. Horizontal lines have a slope of 0 because there is no vertical change, while vertical lines have an undefined slope because the horizontal change is 0.

A) The pair (-3, 0) and slope = 2/3 represents a line with a slope of 2/3.

B) The point (2, -2) is on a line with a slope of 1.

C) The pair (6, 2) and (-3, -7) does not represent a horizontal line because there is a change in both x and y coordinates.

D) There is no pair of points given that represents a vertical line, as vertical lines require the x-coordinates to be the same while the y-coordinates change.

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