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Determine the equation for a line passing through (0,7) and (0,-8).

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Final answer:

The equation for the line passing through the points (0,7) and (0,-8) is x = 0, which represents a vertical line or the y-axis itself.

Step-by-step explanation:

The equation for a line passing through two points can be found using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. However, in this case, both points given have the same x-coordinate (0), which means that the line is vertical. A vertical line cannot be expressed in the slope-intercept form because the slope of a vertical line is undefined. Instead, such a line is described by an equation in the form of x = a constant. Given the points (0,7) and (0,-8), the x-coordinate is consistently 0.

Therefore, the equation for the line passing through these points is x = 0. This line is a vertical line that intersects the y-axis at every possible y-value and it is also known as the y-axis itself. Since the x-value does not change, there is no slope to calculate, and the y-intercept is not a single point but rather the entire line itself.

Finally, if we were tasked to calculate the slope of a line like in the question involving the points (1, 0.1) and (7, 26.8), we would use the formula for slope (m) which is (y2 - y1) / (x2 - x1). However, this is not applicable to the current problem since the line is vertical.

User Nick Sinas
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