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What is the slope of the dotted lines and the reflection line? And how do I find it?

A) The slope of the dotted lines is 0, and the reflection line is horizontal.
B) The slope of the dotted lines is undefined, and the reflection line is vertical.
C) The slope of the dotted lines is 1, and the reflection line is diagonal.
D) The slope of the dotted lines is -1, and the reflection line is diagonal.

User Shonzilla
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1 Answer

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Final answer:

The slope of a horizontal line is 0 because there's no vertical change as the x-value increases, while the slope of a vertical line is undefined due to a zero horizontal change. A diagonal line's slope depends on its direction and steepness, with a positive slope indicating an upward trend and a negative slope indicating a downward trend.

Step-by-step explanation:

To determine the slope of the dotted lines and reflection line, we need to refer to the definitions and characteristics of lines and their slopes. The slope is a measure of how steep a line is and is calculated as the rise over the run, which is the change in the y-values divided by the change in the x-values of two points on the line.

A horizontal line has a slope of 0 because there is no rise, the y-value does not change as the x-value increases. A vertical line has an undefined slope because the run is 0, so you would be dividing by zero, which is not possible. When a line has a positive slope, you can see the line move upwards as you move from left to right, meaning as the x-value increases, so does the y-value. In contrast, a line with a negative slope moves downwards as you move from left to right.

Given the options, if the dotted lines are horizontal, they would have a slope of 0 (Option A). If the dotted lines are vertical, they would have an undefined slope (Option B). If the reflection line is diagonal with an equal angle relative to the x-axis and y-axis, it would be reasonable to assume a slope of 1 or -1 (Options C and D). Without a graph to examine, we would match each description with the known properties of lines: horizontal lines have a slope of 0, vertical lines have an undefined slope, and diagonal lines have slopes that can be determined by their steepness and direction.

User Heyred
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